My name in books

My name in title from Math Reviews

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My publications

Vaserstein in title from Math. Reviews 10 items

MR3144594 Rao, Dhvanita R.; Gupta, Neena; On the non-injectivity of the Vaserstein symbol in dimension three. J. Algebra 399 (2014), 378–388.

MR0882802 (88m:18020) van der Kallen, Wilberd Vaserstein's pre-stabilization theorem over commutative rings. Comm. Algebra 15 (1987), no. 3, 657--663. (Reviewer: Roger C. Alperin) 18F25 (16A54 19B10)

MR1113961 (92k:19001a) Hinson, Edward K. On Vaserstein's power operation on elementary orbits. Comm. Algebra 19 (1991), no. 6, 1851--1854. (Reviewer: Charles Weibel) 19B99 (20H25)

MR1155684 (92k:19001b) Hinson, Edward K. On Vaserstein's power operation on elementary orbits. Comm. Algebra 20 (1992), no. 1, 303--307. (Reviewer: Charles Weibel) 19B99 (20H25)

MR1352866 (96j:11028) Zhang, Zhao Ji On a problem of Vaserstein. (Chinese) Zhejiang Daxue Xuebao Ziran Kexue Ban 28 (1994), no. 5, 608--611. (Reviewer: Qi Sun) 11C20 (11A05)  Zbl 0838.11022

MR1701386 (2000f:60019) Abdellaoui, Taoufiq Approximation de la $L^1$-distance de Wasserstein. (French) [Approximation of $L^1$-Vaserstein distance] C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 12, 1203--1206. 60E05

MR2473300 (2010a:32022) Ivarsson, Björn; Kutzschebauch, Frank A solution of Gromov's Vaserstein problem. C. R. Math. Acad. Sci. Paris 346 (2008), no. 23-24, 1239--1243. (Reviewer: Sergey Ivashkovich) 32E10 (15A23 15A54). Zbl 1160.32017

MR2749274 Vavilov, N. A.; Sinchuk, S. S. Decompositions of Dennis-Vaserstein type. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 375 (2010), Voprosy Teorii Predstavlenii Algebr i Grupp. 19, 48–60, 210, 20G35

Dennis-Vaserstein type decompositions = Разложения типа Денниса–Васерштейна

MR3071388 Butkovsky, O. A.; Veretennikov, A. Yu.; On asymptotics for Vaserstein coupling of Markov chains. Stochastic Process. Appl. 123 (2013), no. 9, 3518–3541.

MR3144594 Rao, Dhvanita R.(6-BHAVC); Gupta, Neena(6-ISI-SMU)

On the non-injectivity of the Vaserstein symbol in dimension three. (English summary) 

J. Algebra 399 (2014), 378–388.  13C10 (19B14 19G12)


Vasershtein in title from Math. Reviews 1 item

MR0583946 (82e:62057)  Papantoni-Kazakos, P. The Vasershtein distance as the stability criterion in robust estimation. 

IEEE Trans. Inform. Theory 26 (1980), no. 5, 620--625.  62F35

In the models used by Hampel as well as by Gray and the author for the qualitative analysis of robust parameter estimators, the Prohorov stability criterion was used. The Vasershtein distance is proposed here as an alternative stability measure. This measure, in contrast to the Prohorov criterion, implies performance stability of the estimators and leads to a constructive analysis for exponentially fast convergence.

Vasserstein in title from Math. Reviews 2 items

MR1015898 (90k:82006) Kirillov, A. B.; Rădulescu, D. C.; Styer, D. F. Vasserstein distances in two-state systems. J. Statist. Phys. 56 (1989), no. 5-6, 931--937. (Reviewer: Milos Zahradnik) 82A05 (82A68)

Abstract We present formulas for the Vasserstein distance between two statistical 

mechanical states of a two-state system. For example, in a ferromagnetic spin-1/2 Ising 

model the Vasserstein distance is half the difference in the magnetizations.

MR0328982 (48 #7324) Vallander, S. S. Calculations of the Vasseršteĭn distance between probability distributions on the line. (Russian) Teor. Verojatnost. i Primenen. 18 (1973), 824--827. (Reviewer: I. Csiszar) 60B05.  English translation: Theory Probab. Appl., 18(4), 784–786. (3 pages)

Abstract: We prove that the Wasserstein distance between probability distributions on the line

coincides with the $L^1$-distance between their distribution function. ...

Wasserstein in title from Math. Reviews

Wasserstein in title from Math. Reviews 1978-1999  17 items

MR0536797 (80d:62004b) Transactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes. Vol. B.  Held in Prague, August 28–September 1, 1978. D. Reidel Publishing Co., Dordrecht-Boston, Mass., 1978. 402 pp. ISBN: 90-277-0913-0  62-06 (60-06 90-06 93Exx 94Axx)

MR0536824 (81e:60003) Szulga, Alicja On the Wasserstein metric. Transactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1978), Vol. B, pp. 267--273, Reidel, Dordrecht-Boston, Mass., 1978. (Reviewer: V. J. Paulauskas) 60B05 (90A05)

MR0752258 (85m:60009) Givens, Clark R.; Shortt, Rae Michael A class of Wasserstein metrics for probability distributions. Michigan Math. J. 31 (1984), no. 2, 231--240. (Reviewer: R. M. Dudley) 60B10 (60E15)

MR0795791 (86m:60004) Rüschendorf, Ludger The Wasserstein distance and approximation theorems. Z. Wahrsch. Verw. Gebiete 70 (1985), no. 1, 117--129. (Reviewer: S. T. Rachev) 60A10 (60B10 60G05)

MR1009457 (90k:60029) Cuesta, Juan Antonio; Matrán, Carlos Notes on the Wasserstein metric in Hilbert spaces. Ann. Probab. 17 (1989), no. 3, 1264--1276. (Reviewer: S. T. Rachev) 60E05 (60B05 60B12)

MR1074632 (92d:60007) Rachev, S. T.; Shortt, R. M. Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals. Dissertationes Math. (Rozprawy Mat.) 299 (1990), 35 pp. (Reviewer: Donald L. Cohn) 60B10 (60F05 60F17)

MR1127323 (93a:62081) Gelbrich, Matthias On a formula for the $L^2$ Wasserstein metric between measures on Euclidean and Hilbert spaces. Math. Nachr. 147 (1990), 185--203. (Reviewer: Juan A. Cuesta-Albertos) 62H05 (60B11 62E10)

MR1209844 (93m:60194) Simonot, François Analyse de la stabilité de systèmes de stockage par la métrique de Wasserstein. (French) [Analysis of the stability of storage systems using the Vaserstein metric] Statist. Anal. Données 16 (1991), no. 3, 183--201. 60K30

MR1165653 (93h:60010) Cuesta, Juan A.; Matrán, Carlos A review on strong convergence of weighted sums of random elements based on Wasserstein metrics. J. Statist. Plann. Inference 30 (1992), no. 3, 359--370. (Reviewer: A. Bozorgnia) 60B12 (60B11)

MR1207216 (94a:60019) Tuero, Araceli On the stochastic convergence of representations based on Wasserstein metrics. Ann. Probab. 21 (1993), no. 1, 72--85. (Reviewer: Ludger Rüschendorf) 60E05 (60B10)

MR1297788 (95i:60026) Cuesta-Albertos, Juan A.; Matrán-Bea, Carlos Stochastic convergence through Skorohod representation theorems and Wasserstein distances. First International Conference on Stochastic Geometry, Convex Bodies and Empirical Measures (Palermo, 1993). Rend. Circ. Mat. Palermo (2) Suppl. No. 35 (1994), 89--113. (Reviewer: Mindaugas Bloznelis) 60F15 (60B11 60B12 60F25)

MR1329874 (96d:60020) Horowitz, Joseph; Karandikar, Rajeeva L. Mean rates of convergence of empirical measures in the Wasserstein metric. J. Comput. Appl. Math. 55 (1994), no. 3, 261--273. (Reviewer: Joseph E. Yukich) 60D05 (60C05)

MR1385397 (97d:60025) Cuesta-Albertos, J. A.; Matrán-Bea, C.; Tuero-Diaz, A. On lower bounds for the $L^2$-Wasserstein metric in a Hilbert space. J. Theoret. Probab. 9 (1996), no. 2, 263--283. (Reviewer: Ludger Rüschendorf) 60E15

MR1485526 (98g:60105) Gelbrich, Matthias; Rachev, Svetlozar T. Discretization for stochastic differential equations, $L^p$ Wasserstein metrics, and econometrical models. Distributions with fixed marginals and related topics (Seattle, WA, 1993), 97--119, IMS Lecture Notes Monogr. Ser., 28, Inst. Math. Statist., Hayward, CA, 1996. 60H10 (60F17)

MR1698999 (2000g:60034) del Barrio, Eustasio; Giné, Evarist; Matrán, Carlos Central limit theorems for the Wasserstein distance between the empirical and the true distributions. Ann. Probab. 27 (1999), no. 2, 1009--1071. (Reviewer: Lajos Horváth) 60F05 (60B12 62E20). Zentralblatt MATH: 0958.60012. Cited by 45

MR1701386 (2000f:60019) Abdellaoui, Taoufiq Approximation de la $L^1$-distance de Wasserstein. (French) [Approximation of $L^1$-Vaserstein distance] C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 12, 1203--1206. 60E05

MR1726488 (2000k:65173) Kinderlehrer, David; Walkington, Noel J. Approximation of parabolic equations using the Wasserstein metric. M2AN Math. Model. Numer. Anal. 33 (1999), no. 4, 837--852. (Reviewer: Wilfrid Gangbo) 65M60 (35A35)

MR1740113 (2001a:60024) del Barrio, Eustasio; Cuesta-Albertos, Juan A.; Matrán, Carlos; Rodríguez-Rodríguez, Jesús M. Tests of goodness of fit based on the $L_2$-Wasserstein distance. Ann. Statist. 27 (1999), no. 4, 1230--1239. (Reviewer: Lajos Horváth) 60F05 (60F25 62E20)

Wasserstein in title from Math. Reviews 2000-2003   11 items 

MR1769953 (2001b:60008) Belili, Nacereddine; Heinich, Henri Distances de Wasserstein et de Zolotarev. (French) [Wasserstein and Zolotarev distances] C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 9, 811--814. 60B10 (60E05)

MR1784174 (2002b:60055) Mikami, T. Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric. Appl. Math. Optim. 42 (2000), no. 2, 203--227. (Reviewer: Shuenn Jyi Sheu) 60F15 (60H30 82C35)

MR1788425 (2002k:94006) Gangbo, Wilfrid; McCann, Robert J. Shape recognition via Wasserstein distance. Quart. Appl. Math. 58 (2000), no. 4, 705--737. 94A08 (28A35 49Q20).  Zbl 1039.49038 

MR1865668 (2002h:49069) Benamou, J. D.; Brenier, Y. Mixed $L^2$-Wasserstein optimal mapping between prescribed density functions. J. Optim. Theory Appl. 111 (2001), no. 2, 255--271. 49Q20 (49M30 65K10)

MR1878316 (2003d:46087) Biane, P.; Voiculescu, D. A free probability analogue of the Wasserstein metric on the trace-state space. Geom. Funct. Anal. 11 (2001), no. 6, 1125--1138. (Reviewer: Dimitri Y. Shlyakhtenko) 46L54

MR1915779 (2003d:62061) de Wet, T. Goodness-of-fit tests for location and scale families based on a weighted $L_2$-Wasserstein distance measure. Test 11 (2002), no. 1, 89--107. 62F05 (60G15 62E20). Zentralblatt MATH: 1037.62007

MR1936827 (2003h:28006) Belili, Nacereddine; Heinich, Henri Approximation pour la distance de Wasserstein. (French) [Approximation for the Wasserstein distance] C. R. Math. Acad. Sci. Paris 335 (2002), no. 6, 537--540. (Reviewer: Klaus D. Schmidt) 28A33 (60A10)

MR2058979 (2005k:62030) Cuesta-Albertos, Juan A.; Matrán Bea, Carlos; Rodríguez Rodríguez, Jesús M. Shape of a distribution through the $L_2$-Wasserstein distance. Distributions with given marginals and statistical modelling, 51--61, Kluwer Acad. Publ., Dordrecht, 2002. 62E10 (62E17 62H05)

MR1964961 (2004b:60060) del Barrio, Eustasio; Giné, Evarist; Matrán, Carlos Correction: ``Central limit theorems for the Wasserstein distance between the empirical and the true distributions'' [Ann. Probab. 27 (1999), no. 2, 1009--1071; MR1698999 (2000g:60034)]. Ann. Probab. 31 (2003), no. 2, 1142--1143. 60F05 (60B12 62E20)

MR1983782 (2004c:49027) Carlen, E. A.; Gangbo, W. Constrained steepest descent in the 2-Wasserstein metric. Ann. of Math. (2) 157 (2003), no. 3, 807--846. (Reviewer: Luigi De Pascale) 49J45 (35Q99 49J10 60H15 82C35)

MR2073437 (2005f:60056) Haeusler, Erich; Mason, David M. Asymptotic distributions of trimmed Wasserstein distances between the true and the empirical distribution function. Stochastic inequalities and applications, 279--298, Progr. Probab., 56, Birkhäuser, Basel, 2003. (Reviewer: Lajos Horváth) 60F05 (62G30)

Wasserstein in title from Math. Reviews 2004-2006 12  items 

MR2048566 (2005b:82075) Carlen, E. A.; Gangbo, W. Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric. Arch. Ration. Mech. Anal. 172 (2004), no. 1, 21--64. (Reviewer: Laurent E. Gosse) 82C40 (35D05 35K15 82C31)

MR2094049 (2005k:60231) Gibbs, Alison L. Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration. Stoch. Models 20 (2004), no. 4, 473--492. (Reviewer: John P. Lehoczky) 60J20 (62M40)

MR2091496 (2005h:35304) Di Francesco, Marco; Markowich, Peter A. Entropy dissipation and Wasserstein metric methods for the viscous Burgers' equation: convergence to diffusive waves. Partial differential equations and inverse problems, 145--165, Contemp. Math., 362, Amer. Math. Soc., Providence, RI, 2004. (Reviewer: Alp O. Eden) 35Q53 (35B40 35K55)

MR2163983 (2006c:35147) Carrillo, J. A.; Toscani, G. Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends in mathematical physics, 234--244, World Sci. Publ., Hackensack, NJ, 2004. 35K57 (35B40 45K05 76T25 82C40 82C70)

MR2121458 (2005k:62135) del Barrio, Eustasio; Giné, Evarist; Utzet, Frederic Asymptotics for $L_2$ functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances. Bernoulli 11 (2005), no. 1, 131--189. (Reviewer: Lajos Horváth) 62G30 (60F05). Zbl 1063.62072

MR2192294 (2007c:28003) Otto, Felix; Westdickenberg, Michael Eulerian calculus for the contraction in the Wasserstein distance. SIAM J. Math. Anal. 37 (2005), no. 4, 1227--1255 (electronic). 28A33

MR2305058 Ambrosio, L. Gradient flows in metric spaces and in the Wasserstein space of probability measures. (Italian) Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 29 (2005), no. 1, 15--33. 28A33 (49Q20)

MR2148889 (2006i:35052) Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe Gradient flows with metric and differentiable structures, and applications to the Wasserstein space. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 15 (2004), no. 3-4, 327--343. (Reviewer: Gong Qing Zhang) 35J20 (28A33 35A15)

MR2209130 (2006j:76121) Carrillo, José A.; McCann, Robert J.; Villani, Cédric Contractions in the 2-Wasserstein length space and thermalization of granular media. Arch. Ration. Mech. Anal. 179 (2006), no. 2, 217--263. (Reviewer: Benoˆıt P. Desjardins) 76M30 (35K57 58E50 76T25 82C40)

MR2250166 (2007j:49051) Brancolini, A.; Buttazzo, G.; Santambrogio, F. Path functionals over Wasserstein spaces. J. Eur. Math. Soc. (JEMS) 8 (2006), no. 3, 415--434. (Reviewer: Luigi De Pascale) 49Q20 (28A33 49J45 58E10 90B10). Zbl 1130.49036 

MR2274850 (2008f:62025) Barbour, A. D.; Xia, Aihua On Stein's factors for Poisson approximation in Wasserstein distance. Bernoulli 12 (2006), no. 6, 943--954. (Reviewer: Dominic Schuhmacher) 62E17

MR2287892 (2007k:35315) Carrillo, José A.; Di Francesco, Marco; Lattanzio, Corrado Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws. J. Differential Equations 231 (2006), no. 2, 425--458. (Reviewer: Yu. G. Rykov) 35L65 (35B40)

Wasserstein in title from Math. Reviews 2007  5 items 

MR2255281 (2007k:35255) Carrillo, J. A.; Di Francesco, M.; Toscani, G. Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering. Proc. Amer. Math. Soc. 135 (2007), no. 2, 353--363 (electronic). (Reviewer: Ross Pinsky) 35K57 (35B40 35K15)

MR2267755 (2007k:49001) Lisini, Stefano Characterization of absolutely continuous curves in Wasserstein spaces. Calc. Var. Partial Differential Equations 28 (2007), no. 1, 85--120. (Reviewer: Paul Raynaud de Fitte) 49J10 (28A33 35Q35 49Q20)

MR2314463 (2008m:49206) Ambrosio, Luigi; Santambrogio, Filippo Necessary optimality conditions for geodesics in weighted Wasserstein spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007), no. 1, 23--37. 49Q20 (35K55 49K05 76M30 76N10)

MR2339442 (2009d:35215) Carrillo, J. A.; Di Francesco, M.; Lattanzio, C. Contractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 10 (2007), no. 2, 277--292. 35L65 (28A33)

MR2343987 (2008f:35211) Tudorascu, Adrian Wasserstein kernels for one-dimensional diffusion problems. Nonlinear Anal. 67 (2007), no. 9, 2553--2572. (Reviewer: Toka Diagana) 35K57 (35D05 35R35 49M25)

Wasserstein in title from Math. Reviews 2008 16 items  (see VinTitle2 for for other 13 items)

MR2350420 (2009e:60010) Clement, Philippe; Desch, Wolfgang An elementary proof of the triangle inequality for the Wasserstein metric. Proc. Amer. Math. Soc. 136 (2008), no. 1, 333--339 (electronic). (Reviewer: Luigi De Pascale) 60B05 (49Q20)

MR2361303 (2009b:37101) Ambrosio, Luigi; Gangbo, Wilfred Hamiltonian ODEs in the Wasserstein space of probability measures. Comm. Pure Appl. Math. 61 (2008), no. 1, 18--53. (Reviewer: Cédric Villani) 37J05 (28A33 34F05 49J52 60B10)

MR2358290 (2009b:58014) Lott, John Some geometric calculations on Wasserstein space. Comm. Math. Phys. 277 (2008), no. 2, 423--437. (Reviewer: Cédric Villani) 58B20 (58J65)

MR2386101 (2009g:60007) Decreusefond, L. Wasserstein distance on configuration space. Potential Anal. 28 (2008), no. 3, 283--300. (Reviewer: Ali Süleyman Üstünel) 60B05 (60H07)

MR2389987 (2008m:35140) Tudorascu, Adrian On the Jordan-Kinderlehrer-Otto variational scheme and constrained optimization in the Wasserstein metric. Calc. Var. Partial Differential Equations 32 (2008), no. 2, 155--173. 35K15 (35A15 35A35 46E35 46N20 49J45 49M25)

MR2395521 (2009c:35041) Di Francesco, Marco; Wunsch, Marcus Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models. Monatsh. Math. 154 (2008), no. 1, 39--50. (Reviewer: Fucai Li) 35G25 (35B40 45M05 76X05 82D37)

MR2403310 (2010a:49064) Champion, Thierry; De Pascale, Luigi; Juutinen, Petri The $\infty$-Wasserstein distance: local solutions and existence of optimal transport maps. SIAM J. Math. Anal. 40 (2008), no. 1, 1--20. 49Q20 (49K30)

MR2417812 (2009e:53038) Figalli, A.; Juillet, N. Absolute continuity of Wasserstein geodesics in the Heisenberg group. J. Funct. Anal. 255 (2008), no. 1, 133--141. (Reviewer: Cédric Villani) 53C17 (22E25 49Q15)

MR2443374 (2010b:60009) Clément, Philippe; Desch, Wolfgang Wasserstein metric and subordination. Studia Math. 189 (2008), no. 1, 35--52. (Reviewer: Paul Raynaud de Fitte) 60B05 (28A33 47D06 54E35)

MR2452882 (2009k:58072) Daneri, Sara; Savaré, Giuseppe Eulerian calculus for the displacement convexity in the Wasserstein distance. SIAM J. Math. Anal. 40 (2008), no. 3, 1104--1122. (Reviewer: Chloé Jimenez) 58J65 (49J10)

MR2478676 Hairer, Martin; Mattingly, Jonathan C. Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations. Ann. Probab. 36 (2008), no. 6, 2050--2091. 35Q35 (35R60 47D07 60H15 76D05 76M35)

MR2482206 Ambrosio, Luigi; Gigli, Nicola Construction of the parallel transport in the Wasserstein space. Methods Appl. Anal. 15 (2008), no. 1, 1--29. (Reviewer: Koji Kikuchi) 49Q20 (28A33 35K55 47J35)

MR2483740 Bolley, F. Separability and completeness for the Wasserstein distance. Séminaire de probabilités XLI, 371--377, Lecture Notes in Math., 1934, Springer, Berlin, 2008. 60B05

MR2481677 Gangbo, Wilfrid; Nguyen, Truyen; Tudorascu, Adrian Hamilton-Jacobi equations in the Wasserstein space. Methods Appl. Anal. 15 (2008), no. 2, 155--183. 49L25 (47Jxx 82C40)

MR2487455 Walczuk, Anna Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric. [Central limit theorem for an additive functional of a Markov process, stable in the Wasserstein metric] Ann. Univ. Mariae Curie-Skƚodowska Sect. A 62 (2008), 149--159. 60J25 (60F05)

MR2509579 Verde, Rosanna; Irpino, Antonio Comparing histogram data using a Mahalanobis-Wasserstein distance. COMPSTAT 2008---Proceedings in Computational Statistics, 77--89, Physica-Verlag/Springer, Heidelberg, 2008. 62G09 (62H11). Zbl 1147.62054

Wasserstein in title from Math. Reviews 2009 15 items (see VinTitle2 for other 17 items)

MR2713745 Kim, Hwa Kil; Hamiltonian systems and the calculus of differential forms on the Wasserstein space. Thesis (Ph.D.)–Georgia Institute of Technology. 2009. 87 pp. ISBN: 978-1109-37242-7, ProQuest LLC, Thesis

MR2599206 (2011d:60108) Schachermayer, Walter; Schmock, Uwe; Teichmann, Josef Non-monotone convergence in the quadratic Wasserstein distance. Séminaire de Probabilités XLII, 131–136, Lecture Notes in Math., 1979, Springer, Berlin, 2009. (Reviewer: Liviu Constantin Florescu), 60F99 (28A99 91B24)

MR2503990 Ohta, Shin-ichi Gradient flows on Wasserstein spaces over compact Alexandrov spaces. Amer. J. Math. 131 (2009), no. 2, 475--516. 53Cxx (46Txx)

MR2501322 Xia, Aihua; Zhang, Fuxi Polynomial birth-death distribution approximation in the Wasserstein distance. J. Theoret. Probab. 22 (2009), no. 2, 294--310. 60F05 (60J27)

MR2505360 Gangbo, W.; Nguyen, T.; Tudorascu, A. Euler-Poisson systems as action-minimizing paths in the Wasserstein space. Arch. Ration. Mech. Anal. 192 (2009), no. 3, 419--452. 37J50 (35G30 37N20 58Exx)

MR2523014 Petrelli, Luca; Kearsley, Anthony J. Wasserstein metric convergence method for Fokker-Planck equations with point controls. Appl. Math. Lett. 22 (2009), no. 7, 1130--1135. 35K20 (49J45)

MR2520126 Döring, Maik; Stannat, Wilhelm The logarithmic Sobolev inequality for the Wasserstein diffusion. Probab. Theory Related Fields 145 (2009), no. 1-2, 189--209. 31C25 (28Axx 35P15 47D07)

MR2537551 von Renesse, Max-K.; Sturm, Karl-Theodor Entropic measure and Wasserstein diffusion. Ann. Probab. 37 (2009), no. 3, 1114--1191. 60G57 (35R60 47D07 58J65 60J60)

MR2542579 Lisini, Stefano Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces. ESAIM Control Optim. Calc. Var. 15 (2009), no. 3, 712--740. 35K57 (28Axx 35B40 35K15)

MR2529165 Dostoglou, S.; Kahl, J. D. Approximation of homogeneous measures in the 2-Wasserstein metric. Math. Phys. Electron. J. 15 (2009), Paper 1, 19 pp. 60B10 (28Axx 35A35 49Q20)

MR2543873 Joulin, Aldéric A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. Bernoulli 15 (2009), no. 2, 532--549. 60J75

MR2543874 Schuhmacher, Dominic Stein's method and Poisson process approximation for a class of Wasserstein metrics. Bernoulli 15 (2009), no. 2, 550--568. 62E17

MR2533926 Gianazza, Ugo; Savaré, Giuseppe; Toscani, Giuseppe The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation. Arch. Ration. Mech. Anal. 194 (2009), no. 1, 133--220. 35Qxx

MR2540269 Natile, Luca; Savaré, Giuseppe A Wasserstein approach to the one-dimensional sticky particle system. SIAM J. Math. Anal. 41 (2009), no. 4, 1340--1365. 35L65 (35L45 35Q35 76N15 82C22)

MR2555474 Hauray, Maxime Wasserstein distances for vortices approximation of Euler-type equations. Math. Models Methods Appl. Sci. 19 (2009), no. 8, 1357--1384. 35Q31 (35L65)


Wasserstein in title from Math. Reviews 2010. 14 items  (see VinTitle2 for other 20  items )

MR2672546 Lisini, Stefano; Marigonda, Antonio On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals. Manuscripta Math. 133 (2010), no. 1-2, 197–224, 49Q20 (49J27 49J40)

MR2655156 Irpino, Antonio; Verde, Rosanna Clustering linear models using Wasserstein distance. Data analysis and classification, 41–48, Stud. Classification Data Anal. Knowledge Organ., Springer, Berlin, 2010, 62H30 (62J05)

MR2652014 Portegies, Jacobus W.; Peletier, Mark A. Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows. Interfaces Free Bound. 12 (2010), no. 2, 121–150, 35Rxx (80Axx 82Dxx)

MR2644919 Bianchini, S.; Brancolini, A. Estimates on path functionals over Wasserstein spaces. SIAM J. Math. Anal. 42 (2010), no. 3, 1179–1217, 49Q20 (28A78 49K27 93B03)

MR2648273 Takatsu, Asuka On Wasserstein geometry of Gaussian measures. Probabilistic approach to geometry, 463–472, Adv. Stud. Pure Math., 57, Math. Soc. Japan, Tokyo, 2010. (Reviewer: Jonathan Henry Jordan), 60D05 (28A33). Zbl 1206.60016   

MR2641767 Erbar, Matthias The heat equation on manifolds as a gradient flow in the Wasserstein space. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010), no. 1, 1–23, 35A15 (58J35 58J65 60J60)

MR2606878 (2011b:60224) Andres, Sebastian; von Renesse, Max-K. Particle approximation of the Wasserstein diffusion. J. Funct. Anal. 258 (2010), no. 11, 3879–3905. (Reviewer: Nikita Y. Ratanov), 60H10 (60J25 60J68 60K35)

MR2606871 Kuwada, Kazumasa Duality on gradient estimates and Wasserstein controls. J. Funct. Anal. 258 (2010), no. 11, 3758–3774. (Reviewer: Po-Lam Yung), 35H20 (35R01 35R03 47D03 53C44 60J60)

MR2593592 (2010k:60106) Wang, Ran; Wang, Xinyi; Wu, Liming Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition. Statist. Probab. Lett. 80 (2010), no. 5-6, 505–512, 60F10

MR2580956 (2011a:35237) Cavalli, Fausto; Naldi, Giovanni A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation. Kinet. Relat. Models 3 (2010), no. 1, 123–142, 35K55 (35B25 65M06)

MR2574738 Andres, Shizan; Shao, Jinghai; Sturm, Karl-Theodor Wasserstein space over the Wiener space. Probab. Theory Related Fields 146 (2010), no. 3-4, 535–565. (Reviewer: Hélène Airault), 60J45 (58B20 60H07)

MR2752678 Granieri, Luca Metric currents and geometry of Wasserstein spaces. Rend. Semin. Mat. Univ. Padova 124 (2010), 91–125. ISBN: 978-88-7784-325-8, 37J50 (49Q20)

MR2730652 Madras, Neal; Sezer, Deniz Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances. Bernoulli 16 (2010), no. 3, 882–908, 60J22

MR2731158 (2011h:53045) Kloeckner, Benoît A geometric study of Wasserstein spaces: Euclidean spaces. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9 (2010), no. 2, 297–323. (Reviewer: Nicolas Juillet), 53C23 (28A33 49Q05)

Vaserstein in title MR 2010

MR2749274 (2012a:20082)   Vavilov, N. A.(RS-STPT); Sinchuk, S. S.(RS-STPT)

Decompositions of Dennis-Vaserstein type. (Russian. English, Russian summary) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 375 (2010), Voprosy Teorii Predstavlenii Algebr i Grupp. 19, 48--60, 210; translation in 

J. Math. Sci. (N. Y.) 171 (2010), no. 3, 331–337 

Wasserstein in title from Math. Reviews 2011, 17  items (see VinTitle2 for other 29 items)

MR2801182 Agueh, Martial; Carlier, Guillaume Barycenters in the Wasserstein space. SIAM J. Math. Anal. 43 (2011), no. 2, 904–924, 49Q20 (28A33 49K10 60D99).  Zbl 1223.49045

MR2799600 Lipman, Y.; Daubechies, I. Conformal Wasserstein distances: comparing surfaces in polynomial time. Adv. Math. 227 (2011), no. 3, 1047–1077, 53C23.  Zbl 1217.53026

MR2799815 Shao, Jinghai Transportation cost inequalities for Wasserstein diffusions. Bull. Sci. Math. 135 (2011), no. 4, 383–394, 60J68 (28A33 47D07 58Jxx 60J35).  Zbl 1221.60118

MR2808856 Gangbo, Wilfrid; Kim, Hwa Kil; Pacini, Tommaso Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems. Mem. Amer. Math. Soc. 211 (2011), no. 993, vi+77 pp. ISBN: 978-0-8218-4939-2, 37Kxx (53Dxx 58Axx).  Zbl 1221.53001

MR2784570 Mémoli, Facundo A spectral notion of Gromov-Wasserstein distance and related methods. Appl. Comput. Harmon. Anal. 30 (2011), no. 3, 363–401, 53Cxx (49Q20).  Zbl 1219.53046

MR2811584  Mémoli, Facundo Gromov-Wasserstein distances and the metric approach to object matching. Found. Comput. Math. 11 (2011), no. 4, 417–487. 68T10 (49Q15 54E35 60B05 60B10 68U10)

MR2740101 Muskulus, Michael; Verduyn-Lunel, Sjoerd Wasserstein distances in the analysis of time series and dynamical systems. Phys. D 240 (2011), no. 1, 45–58, 37M10 (60G35 62M10).  Zbl 1214.37054

MR2815689 Herrmann, Michael; Niethammer, Barbara Kramers' formula for chemical reactions in the context of Wasserstein gradient flows. Commun. Math. Sci. 9 (2011), no. 2, 623–635, 35Q84 (35B25 49S05 80Axx). Zbl 1219.35315

MR2811584 Mémoli, Facundo Gromov-Wasserstein distances and the metric approach to object matching. Found. Comput. Math. 11 (2011), no. 4, 417–487, 68T10 (49Q15 54E35 60B05 60B10 68U10).  Zbl pre05977706

MR2861675  Boissard, Emmanuel Simple bounds for convergence of empirical and occupation measures in 1-Wasserstein distance. Electron. J. Probab. 16 (2011), no. 83, 2296–2333. 60B10 (39B72).  Zbl pre06049139. Published: NOV 15 2011

MR2871291  Takatsu, Asuka Wasserstein geometry of Gaussian measures. Osaka J. Math. 48 (2011), no. 4, 1005–1026. 53Cxx (60D05 60G15).  Zbl pre06006848. Published: DEC 2011.  pdf

MR2857030  Stannat, Wilhelm Functional inequalities for the Wasserstein Dirichlet form. Seminar on Stochastic Analysis, Random Fields and Applications VI, 245–260, Progr. Probab., 63, Birkhäuser/Springer Basel AG, Basel, 2011. (Reviewer: Ren Ming Song) 60J60 (28A33 35A23 35P15 47D07 58J65 60J35)

MR2851684  Caillerie, Claire; Chazal, Frédéric; Dedecker, Jérôme; Michel, Bertrand Deconvolution for the Wasserstein metric and geometric inference. Electron. J. Stat. 5 (2011), 1394–1423. (Reviewer: Vera Pawlowsky-Glahn) 62H12 (28A33 60B10 60D99 62G07 62G99)

MR2843007  Eberle, Andreas Reflection coupling and Wasserstein contractivity without convexity. C. R. Math. Acad. Sci. Paris 349 (2011), no. 19-20, 1101–1104. 60J60.   Zbl 05966335 . Published: OCT 2011

MR2842966  Adams, Stefan; Dirr, Nicolas; Peletier, Mark A.; Zimmer, Johannes From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage. Comm. Math. Phys. 307 (2011), no. 3, 791–815. (Reviewer: Boualem Djehiche) 60K35 (60F10). Zbl 05977587 .   Published: NOV 2011

MR2838101  Sturm, Karl-Theodor Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions. Bull. Sci. Math. 135 (2011), no. 6-7, 795–802. 60B05 (46E30).  Zbl 05970569   . Published: SEP-NOV 2011

MR2812740  Kreitmeier, Wolfgang Optimal vector quantization in terms of Wasserstein distance. J. Multivariate Anal. 102 (2011), no. 8, 1225–1239. 60E05 (60B05 62E17 68P30 94A17 94A29). Zbl 05918992.  Zbl 05918992   .  Published: SEP 2011

Wasserstein in title from Math. Reviews 2012, 12 items (see VinTitle2 for other 40 items)

MR3098634   Santambrogio, Filippo Gradient flows in Wasserstein spaces and applications to crowd movement. Seminaire: Equations aux Dérivées Partielles. 2009–2010, Exp. No. XXVII, 16 pp., Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau, 2012. 49Q20 (35F15 35Q84)

MR2949241   Takatsu, Asuka; Yokota, Takumi Cone structure of L2-Wasserstein spaces. J. Topol. Anal. 4 (2012), no. 2, 237–253. 58Bxx (28A33 53Cxx)

MR2994677  Gigli, Nicola; Ohta, Shin-Ichi; First Variation Formula in Wasserstein Spaces over Compact Alexandrov Spaces. Canad. Math. Bull. 55 (2012), no. 4, 723–735. pdf

MR2964689  Bolley, François; Gentil, Ivan; Guillin, Arnaud; Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations. J. Funct. Anal. 263 (2012), no. 8, 2430–2457.  Arxiv preprint arXiv:1110.3606, 2011 -

MR2921976   Komorowski, Tomasz; Walczuk, Anna Central limit theorem for Markov processes with spectral gap in the Wasserstein metric. Stochastic Process. Appl. 122 (2012), no. 5, 2155–2184. 60J25 (60B12 60F05 60J35). Published: MAY 2012

MR2921215  Lisini, Stefano; Matthes, Daniel; Savaré, Giuseppe Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. J. Differential Equations 253 (2012), no. 2, 814–850. 35K35 (35A15)

Published: JUL 15 2012

MR2915328  Arnrich, Steffen; Mielke, Alexander; Peletier, Mark A.; Savaré, Giuseppe; Veneroni, Marco Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction. Calc. Var. Partial Differential Equations 44 (2012), no. 3-4, 419–454. 35Q84 (35B25 49S05 70F40 70G75). Published: JUL 2012

MR2901195  Takatsu, Asuka Wasserstein geometry of porous medium equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 2, 217–232. 35K57 (28A75 35C06 46E27 60D05). Published: MAR-APR 2012

MR2900478  Chodosh, Otis A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval. J. Funct. Anal. 262 (2012), no. 10, 4570–4581. 53Cxx (58Dxx 60B05)

MR2887832  Agueh, Martial Finsler structure in the p-Wasserstein space and gradient flows. C. R. Math. Acad. Sci. Paris 350 (2012), no. 1-2, 35–40. (Reviewer: Benoît Kloeckner) 49Q20 (53C60 58B20)/  Published: JAN 2012

MR2949240  Kloeckner, Benoît A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces. J. Topol. Anal. 4 (2012), no. 2, 203–235. 58Dxx (28A78 60B05)

MR3021775   Bertrand, Jérôme; Kloeckner, Benoît A geometric study of Wasserstein spaces: Hadamard spaces. J. Topol. Anal. 4 (2012), no. 4, 515–542. 53C21 (28A33 49Q20)

Wasserstein in title from Math. Reviews 2013  17 items

MR3380344  Stannat, Wilhelm Two remarks on the Wasserstein Dirichlet form. Seminar on Stochastic Analysis, Random Fields and Applications VII, 235–255, Progr. Probab., 67, Birkhäuser/Springer, Basel, 2013. 60J60 (31C25 58J65)

MR3182684 Duong, Manh Hong; Laschos, Vaios; Renger, Michiel Wasserstein gradient flows from large deviations of many-particle limits. ESAIM Control Optim. Calc. Var. 19 (2013), no. 4, 1166–1188. 35Q84 (35A15)

MR3126088  Caillerie, Claire; Chazal, Frédéric; Dedecker, Jérôme; Michel, Bertrand Deconvolution for the Wasserstein metric and geometric inference. Geometric science of information, 561–568, Lecture Notes in Comput. Sci., 8085, Springer, Heidelberg, 2013. 94A17 (53C23)

MR3126071   Benning, Martin; Calatroni, Luca; Düring, Bertram; Schönlieb, Carola-Bibiane A primal-dual approach for a total variation Wasserstein flow. Geometric science of information, 413–421, Lecture Notes in Comput. Sci., 8085, Springer, Heidelberg, 2013. 35K30 (35K59 49Q20)

MR3126070  Bertrand, Jérôme; Kloeckner, Benoît R. A geometric study of Wasserstein spaces: an addendum on the boundary. Geometric science of information, 405–412, Lecture Notes in Comput. Sci., 8085, Springer, Heidelberg, 2013. 53C23 (28A33 49Q20)

MR3039437  Schmitzer, Bernhard; Schnörr, Christoph Modelling convex shape priors and matching based on the Gromov-Wasserstein distance. J. Math. Imaging Vision 46 (2013), no. 1, 143–159. 68U10 (94A08)

MR3092749  Takatsu, Asuka Behaviors of φ-exponential distributions in Wasserstein geometry and an evolution equation. SIAM J. Math. Anal. 45 (2013), no. 4, 2546–2556. 60E05 (60B05 60D99)

MR3048643 Agueh, Martial; Bowles, Malcolm; One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces. Acta Appl. Math. 125 (2013), 121–134.

MR3044136  Gigli, Nicola; Otto, Felix Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric. Calc. Var. Partial Differential Equations 47 (2013), no. 1-2, 181–206. 76S05 (35Q35 49Q20)

MR2983027 Lipman, Y.; Puente, J.; Daubechies, I.; Conformal Wasserstein distance: II. computational aspects and extensions. Math. Comp. 82 (2013), no. 281, 331–381.

MR3029241 Piccoli, Benedetto; Rossi, Francesco; Transport Equation with Nonlocal Velocity in Wasserstein Spaces: Convergence of Numerical Schemes. Acta Appl. Math. 124 (2013), no. 1, 73–105.

MR3017033 Kim, Hwa Kil; Moreau–Yosida approximation and convergence of Hamiltonian systems on Wasserstein space. J. Differential Equations 254 (2013), no. 7, 2861–2876.

MR3092749 Takatsu, Asuka; Behaviors of φ-Exponential Distributions in Wasserstein Geometry and an Evolution Equation. SIAM J. Math. Anal. 45 (2013), no. 4, 2546–2556.

MR3091990 He, Daojiang; Xu, Xingzhong; Zhao, Jianxin; A new procedure for testing normality based on the L2 Wasserstein distance. J. Syst. Sci. Complex. 26 (2013), no. 4, 572–582.

MR3071256  Agredo, Julián A Wasserstein-type distance to measure deviation from equilibrium of quantum Markov semigroups. Open Syst. Inf. Dyn. 20 (2013), no. 2, 1350009, 20 pp. 81R99 (46L35 47D07)

MR3024100  Bassetti, Federico; Perversi, Eleonora Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations. Electron. J. Probab. 18 (2013), no. 6, 35 pp. 60B10 (60E07 60F05 82C40)

MR3189324  Dedecker, Jérôme; Michel, Bertrand Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension. J. Multivariate Anal. 122 (2013), 278–291. 62G05 (62C20)

MR3220453  Kuwada, Kazumasa Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula. Potential theory and its related fields, 61–80, RIMS Kôkyûroku Bessatsu, B43, Res. Inst. Math. Sci. (RIMS), Kyoto, 2013. 60J35 (39B62 49N15 60B10 70H20)

Wasserstein in title from Math. Reviews 2014  15 items

MR3331178  Carrillo, José Antonio; Choi, Young-Pil; Hauray, Maxime The derivation of swarming models: mean-field limit and Wasserstein distances. Collective dynamics from bacteria to crowds, 1–46, CISM Courses and Lectures, 553, Springer, Vienna, 2014. 82C22 (35Q82)

MR3295393 Thesis Craig, Katy; The exponential formula for the Wasserstein metric. Thesis (Ph.D.)–Rutgers The State University of New Jersey - New Brunswick. 2014. 80 pp. ISBN: 978-1321-29355-5, ProQuest LLC

MR3248053 Carlen, Eric A.; Maas, Jan; An Analog of the 2-Wasserstein Metric in Non-Commutative Probability Under Which the Fermionic Fokker–Planck Equation is Gradient Flow for the Entropy. Comm. Math. Phys. 331 (2014), no. 3, 887–926.. Zbl 06341594

MR3189084 Boissard, Emmanuel; Le Gouic, Thibaut; On the mean speed of convergence of empirical and occupation measures in Wasserstein distance. Ann. Inst. Henri Poincaré Probab. Stat. 50 (2014), no. 2, 539–563. Zbl 1294.60005

MR3178490  Butkovsky, Oleg; Subgeometric rates of convergence of Markov processes in the Wasserstein metric. Ann. Appl. Probab. 24 (2014), no. 2, 526–552. Zbl 06291798

MR3206999  Bourne, D. P.; Peletier, M. A.; Theil, F. Optimality of the triangular lattice for a particle system with Wasserstein interaction. Comm. Math. Phys. 329 (2014), no. 1, 117–140. 82D25 (82D60)

Zbl 1294.82006

MR3192034  Cavalletti, Fabio Decomposition of geodesics in the Wasserstein space and the globalization problem. Geom. Funct. Anal. 24 (2014), no. 2, 493–551. 53C23 (53C22)

MR3182620 Indexed Qiao, Motong; Wang, Wei; Ng, Michael Multi-phase texture segmentation using Gabor features histograms based on Wasserstein distance. Commun. Comput. Phys. 15 (2014), no. 5, 1480–1500. 94A08 (68U10)

MR3187785   Engquist, Björn; Froese, Brittany D. Application of the Wasserstein metric to seismic signals. Commun. Math. Sci. 12 (2014), no. 5, 979–988. 86A15 (62P35 65K99 94A12)

MR3182483   Piccoli, Benedetto; Rossi, Francesco Generalized Wasserstein distance and its application to transport equations with source. Arch. Ration. Mech. Anal. 211 (2014), no. 1, 335–358. 49Q20 (28Dxx 35F25). Zbl 06260964

MR3158572  Gangbo, Wilfrid; Tudorascu, Adrian Weak KAM theory on the Wasserstein torus with multidimensional underlying space. Comm. Pure Appl. Math. 67 (2014), no. 3, 408–463. 58D19 (37J40)

MR3121635  Savaré, Giuseppe Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,∞)

metric measure spaces. Discrete Contin. Dyn. Syst. 34 (2014), no. 4, 1641–1661. 49Q20

MR3257364  Ding, Ying; Wasserstein-Divergence transportation inequalities and polynomial concentration inequalities. Statist. Probab. Lett. 94 (2014), 77–85.

MR3250977  Bolley, François; Carrillo, José A.; Nonlinear Diffusion: Geodesic Convexity is Equivalent to Wasserstein Contraction. Comm. Partial Differential Equations 39 (2014), no. 10, 1860–1869.   

MR3205035  Sturm, Karl-Theodorg A monotone approximation to the Wasserstein diffusion. Singular phenomena and scaling in mathematical models, 25–48, Springer, Cham, 2014. 60J60

Wasserstein in title from Math. Reviews 2015  33 items

MR3535537  Ma, Ming; Lei, Na; Su, Kehua; Zhang, Junwei; Wen, Chengfeng; Cui, Li; Fan, Xin; Gu, Xianfeng Surface-based shape classification using Wasserstein distance. Geom. Imaging Comput. 2 (2015), no. 4, 237–255. 49Q20 (53A05 68T10 68U05)

MR3442190  Le Gouic, Thibaut; Loubes, Jean-Michel Barycenter in Wasserstein spaces: existence and consistency. Geometric science of information, 104–108, Lecture Notes in Comput. Sci., 9389, Springer, Cham, 2015. (Reviewer: Sławomir Kolasiński) 60B05 (49Q20 60B10 62H11 94A15)

MR3453299  Döbler, Christian New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods. ALEA Lat. Am. J. Probab. Math. Stat. 12 (2015), no. 2, 863–902. (Reviewer: N. C. Weber) 60F05 (60G50)

MR3436238 Amsaad, Mohamed; Tudorascu, Adrian On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the continuity equation. Indiana Univ. Math. J. 64 (2015), no. 6, 1835–1877. (Reviewer: Alpár Richárd Mészáros) 35L65 (35B30 35F20 37C10 37J99 49Q20 60A10)

MR3434297 Fraser, Jonathan M. First and second moments for self-similar couplings and Wasserstein distances. Math. Nachr. 288 (2015), no. 17-18, 2028–2041. (Reviewer: Balázs Bárány) 28A33 (28A80 42A85 60B05)

MR3434206 Erbar, Matthias; Maas, Jan; Renger, D. R. Michiel From large deviations to Wasserstein gradient flows in multiple dimensions. Electron. Commun. Probab. 20 (2015), no. 89, 12 pp. 60F10 (35A15 35B27 35Q84 35R60 60B10)

MR3424906 Kloeckner, Benoît R.; Lopes, Artur O.; Stadlbauer, Manuel Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps. Nonlinearity 28 (2015), no. 11, 4117–4137. (Reviewer: Diogo Pinheiro) 37A50 (49K45 49Q10)

MR3423268 Revi

ewed Carlier, Guillaume; Oberman, Adam; Oudet, Edouard Numerical methods for matching for teams and Wasserstein barycenters. ESAIM Math. Model. Numer. Anal. 49 (2015), no. 6, 1621–1642. (Reviewer: Alessio Brancolini) 90C05 (49M29 49Q20)

MR3413589 Pending Peyré, Gabriel Entropic approximation of Wasserstein gradient flows. SIAM J. Imaging Sci. 8 (2015), no. 4, 2323–2351. 94A08 (49Q20 68U10 90C25 90C48)

MR3399536 Pending Jin, Chunyin Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space. Nonlinear Anal. 128 (2015), 412–422. 35Q31 (35B30 35L45 76N10)

MR3385156 Kuwada, Kazumasa; Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates. Calc. Var. Partial Differential Equations 54 (2015), no. 1, 127–161.

MR3383341 Fournier, Nicolas; Guillin, Arnaud; On the rate of convergence in Wasserstein distance of the empirical measure. Probab. Theory Related Fields 162 (2015), no. 3-4, 707–738.

MR3377899 Wu, Zong-min; Tian, Zheng; Distribution function estimates by Wasserstein metric and Bernstein approximation for C−1 functions. Appl. Math. J. Chinese Univ. Ser. B 30 (2015), no. 2, 141–150.

MR3356496 Pending Disser, Karoline; Liero, Matthias On gradient structures for Markov chains and the passage to Wasserstein gradient flows. Netw. Heterog. Media 10 (2015), no. 2, 233–253. 35K10 (35K20 35Q84 37L05 49Q20 60J27 65M08)

MR3352761  Hynd, Ryan; Kim, Hwa Kil Value functions in the Wasserstein spaces: finite time horizons. J. Funct. Anal. 269 (2015), no. 4, 968–997. (Reviewer: Luca Granieri) 49Q20 (35D40 35F25 49L25)

MR3342407 Pending Cacciafesta, Federico; de Suzzoni, Anne-Sophie Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure. J. Differential Equations 259 (2015), no. 3, 1024–1067. 35Q53

MR3345406  Schmitzer, Bernhard; Schnörr, Christoph Globally optimal joint image segmentation and shape matching based on Wasserstein modes. J. Math. Imaging Vision 52 (2015), no. 3, 436–458. 94A08

MR3339225 Pending Gentil, Ivan Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold. Potential Anal. 42 (2015), no. 4, 861–873. 58J65 (53B21 58J35)

MR3338654  Barbour, A. D.; Gan, H. L.; Xia, A. Stein factors for negative binomial approximation in Wasserstein distance. Bernoulli 21 (2015), no. 2, 1002–1013. (Reviewer: Fraser Alexander Daly) 60E05 (62E10 62P10)

MR3338645 Pending Boissard, Emmanuel; Le Gouic, Thibaut; Loubes, Jean-Michel Distribution's template estimate with Wasserstein metrics. Bernoulli 21 (2015), no. 2, 740–759. 60A10 (60E05)

MR3325471 Pending Duong, Manh Hong Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation. Asymptot. Anal. 92 (2015), no. 1-2, 85–106. 35K57 (35B27 35K15 49J45)

MR3333967 Pending Kloeckner, Benoît R. A geometric study of Wasserstein spaces: ultrametrics. Mathematika 61 (2015), no. 1, 162–178. 30L05 (37F35 49Q20)

MR3317894  Irpino, Antonio; Verde, Rosanna Linear regression for numeric symbolic variables: a least squares approach based on Wasserstein distance. Adv. Data Anal. Classif. 9 (2015), no. 1, 81–106. 62J05 (46F10 62G30)

MR3314482 Pending Dedecker, Jérôme; Fischer, Aurélie; Michel, Bertrand Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one. Electron. J. Stat. 9 (2015), 234–265. 62G05 (62C20)

MR3304898 Pending Durmus, Alain; Moulines, Éric Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm. Stat. Comput. 25 (2015), no. 1, 5–19. 60J99 (62M05)

MR3304897 Indexed Haario, Heikki Introduction to "Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm'' by A. Durmus, É. Moulines [MR3304898]. Stat. Comput. 25 (2015), no. 1, 3. 60J99 (62M05)

MR3311904 Pending Kamalinejad, Ehsan On local well-posedness of the thin-film equation via the Wasserstein gradient flow. Calc. Var. Partial Differential Equations 52 (2015), no. 3-4, 547–564. 49Q20 (35B30 35K25 35K59 49J52 49K40 76A20)

MR3306430  Agulló-Antolín, Marina; Cuesta-Albertos, J. A.; Lescornel, Hélène; Loubes, Jean-Michel A parametric registration model for warped distributions with Wasserstein's distance. J. Multivariate Anal. 135 (2015), 117–130. 62H10 (62F10)

MR3300482  Bonneel, Nicolas; Rabin, Julien; Peyré, Gabriel; Pfister, Hanspeter Sliced and Radon Wasserstein barycenters of measures. J. Math. Imaging Vision 51 (2015), no. 1, 22–45. 94A08

MR3302526 Pending Hynd, Ryan; Kim, Hwa Kil Infinite horizon value functions in the Wasserstein spaces. J. Differential Equations 258 (2015), no. 6, 1933–1966. 49L20 (35D40 35F21)

MR3294365  Bowles, Malcolm; Agueh, Martial Weak solutions to a fractional Fokker-Planck equation via splitting and Wasserstein gradient flow. Appl. Math. Lett. 42 (2015), 30–35. 35R11 (35D30 35Q84 82C31)

MR3293301 Pending Shao, Jinghai Ergodicity of regime-switching diffusions in Wasserstein distances. Stochastic Process. Appl. 125 (2015), no. 2, 739–758. 60J60 (60B10 60J27)

MR3284787 Indexed Lee, Kooktae; Halder, Abhishek; Bhattacharya, Raktim Performance and robustness analysis of stochastic jump linear systems using Wasserstein metric. Automatica J. IFAC 51 (2015), 341–347. 93E03 (93B35)

Wasserstein in title from Math. Reviews 2016    19  items 

MR3584627 Prelim Choi, Byoung Jin; Ji, Un Cig; Exponential convergence rates for weighted sums in noncommutative probability space. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19 (2016), no. 4, 1650027, 13 pp. Zbl 06645470

MR3573296 Prelim Durmus, Alain; Fort, Gersende; Moulines, Éric; Subgeometric rates of convergence in Wasserstein distance for Markov chains. Ann. Inst. Henri Poincaré Probab. Stat. 52 (2016), no. 4, 1799–1822.

MR3566931 Prelim Anderes, Ethan; Borgwardt, Steffen; Miller, Jacob; Discrete Wasserstein barycenters: optimal transport for discrete data. Math. Methods Oper. Res. 84 (2016), no. 2, 389–409.

MR3564778 Prelim Tartavel, Guillaume; Peyré, Gabriel; Gousseau, Yann; Wasserstein Loss for Image Synthesis and Restoration. SIAM J. Imaging Sci. 9 (2016), no. 4, 1726–1755.

MR3558359 Prelim Loibl, Daniel; Matthes, Daniel; Zinsl, Jonathan; Existence of Weak Solutions to a Class of Fourth Order Partial Differential Equations with Wasserstein Gradient Structure. Potential Anal. 45 (2016), no. 4, 755–776.

MR3551945 Prelim Jourdain, Benjamin; Reygner, Julien; A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data. J. Hyperbolic Differ. Equ. 13 (2016), no. 3, 441–602.

MR3545279 Prelim Rippl, Thomas; Munk, Axel; Sturm, Anja; Limit laws of the empirical Wasserstein distance: Gaussian distributions. J. Multivariate Anal. 151 (2016), 90–109.

MR3544329 Pending Piccoli, Benedetto; Rossi, Francesco On properties of the generalized Wasserstein distance. Arch. Ration. Mech. Anal. 222 (2016), no. 3, 1339–1365. 49Q20 (60B10

MR3531395 Pending Azmoodeh, Ehsan; Peccati, Giovanni; Poly, Guillaume The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds. ALEA Lat. Am. J. Probab. Math. Stat. 13 (2016), no. 2, 659–686. 60G22 (60F05 60F15 60G15 60H07)

MR3539346 Pending Kell, Martin

q-heat flow and the gradient flow of the Renyi entropy in the

p-Wasserstein space. J. Funct. Anal. 271 (2016), no. 8, 2045–2089. 58J35 (35K92 35R01 53C23)

MR3527938 Pending Lisini, Stefano Absolutely continuous curves in extended Wasserstein-Orlicz spaces. ESAIM Control Optim. Calc. Var. 22 (2016), no. 3, 670–687. 49J27 (49Q20)

MR3515734 Pending Polyanskiy, Yury; Wu, Yihong Wasserstein continuity of entropy and outer bounds for interference channels. IEEE Trans. Inform. Theory 62 (2016), no. 7, 3992–4002. 94A17

MR3509929 Pending Bertrand, Jérôme; Kloeckner, Benoît R. A geometric study of Wasserstein spaces: isometric rigidity in negative curvature. Int. Math. Res. Not. IMRN 2016, no. 5, 1368–1386. 58C35 (28A33 53C21)

MR3491556  Álvarez-Esteban, Pedro C.; del Barrio, E.; Cuesta-Albertos, J. A.; Matrán, C. A fixed-point approach to barycenters in Wasserstein space. J. Math. Anal. Appl. 441 (2016), no. 2, 744–762. (Reviewer: Mircea Petrache) 49Q20 (49Q15 60B10 62H11)

MR3489381 Pending Craig, Katy The exponential formula for the Wasserstein metric. ESAIM Control Optim. Calc. Var. 22 (2016), no. 1, 169–187. 49Q20

MR3463787  Hauray, Maxime Uniform contractivity in Wasserstein metric for the original 1D Kac's model. J. Stat. Phys. 162 (2016), no. 6, 1566–1570. 82C40 (60J75 76P05)

MR3474827  Wang, Jian

Lp-Wasserstein distance for stochastic differential equations driven by Lévy processes. Bernoulli 22 (2016), no. 3, 1598–1616. (Reviewer: Ying Hui Dong) 60H10 (60J75)

MR3466197 Pending Cuturi, Marco; Peyré, Gabriel A smoothed dual approach for variational Wasserstein problems. SIAM J. Imaging Sci. 9 (2016), no. 1, 320–343. 94A08 (49Q20 65C50 68U10 90C08 90C25)

MR3451384  Azzam, Jonas; David, Guy; Toro, Tatiana Wasserstein distance and the rectifiability of doubling measures: part I. Math. Ann. 364 (2016), no. 1-2, 151–224. (Reviewer: Matthew Badger) 28A75 (28A12)

Wasserstein in title from Math. Reviews 2017      7  items

MR3590527 Prelim Kim, Young-Heon; Pass, Brendan; Wasserstein barycenters over Riemannian manifolds. Adv. Math. 307 (2017), 640–683.

MR3595479 Pending Carfora, Mauro The Wasserstein geometry of nonlinear

σ models and the Hamilton-Perelman Ricci flow. Rev. Math. Phys. 29 (2017), no. 1, 1750001, 71 pp. 53C44 (58D25 58D30 81T17)

MR3598633 Prelim Xiang, Jim X.; Sample size determination of a nonparametric test based on weighted

L2-Wasserstein distance. Statist. Probab. Lett. 123 (2017), 160–164. 62G10 (62G20)

MR3601616 Prelim Berckmoes, Ben; Hellemans, Tim; Sioen, Mark; Van Casteren, Jan; An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric. J. Math. Anal. Appl. 449 (2017), no. 2, 1770–1789. 54B30 (54E05)

MR3606415 Prelim Barbu, Viorel; The Steepest Descent Algorithm in Wasserstein Metric for the Sandpile Model of Self-Organized Criticality. SIAM J. Control Optim. 55 (2017), no. 1, 413–428. 35K59 (35A15 35K15 35R70 60J60)

MR3606732 Prelim Bigot, Jérémie; Gouet, Raúl; Klein, Thierry; López, Alfredo; Geodesic PCA in the Wasserstein space by convex PCA. Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017), no. 1, 1–26. 62H25 (62G05 62G20 62P10)

MR3621265 Prelim Legendre, Guillaume; Turinici, Gabriel; Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces. C. R. Math. Acad. Sci. Paris 355 (2017), no. 3, 345–353.



222  items total 


203 Wasserstein 

10 Vaserstein

1 Vasershtein

2 Vasserstein