Petrelli, L, Tudorascu, A Variational principle for general diffusion problems APPL MATH OPT 50 (3): 229-257 OCT 2004 Hiai, F, Petz, D, Ueda, Y Free transportation cost inequalities via random matrix approximation PROBAB THEORY REL 130 (2): 199-221 OCT 2004 Hiai, F, Petz, D, Ueda, Y Free transportation cost inequalities via random matrix approximation PROBAB THEORY REL 130 (2): 199-221 OCT 2004 Hairer, M, Pavliotis, GA Periodic homogenization for hypoelliptic diffusions J STAT PHYS 117 (1-2): 261-279 OCT 2004 Marton, K Measure concentration for Euclidean distance in the case of dependent random variables ANN PROBAB 32 (3B): 2526-2544 JUL 2004 Chen, LHY, Xia, AH Stein's method, palm theory and poisson process approximation ANN PROBAB 32 (3B): 2545-2569 JUL 2004 = Stein's method, Palm theory and Poisson process approximation Xia, Aihua / Chen, Louis H. Y., The Annals of Probability, Jul 2004 ...particular metric, thereby allowing wider applicability. A Wasserstein pseudometric is introduced for measuring the accuracy of...the total variation distance for random variables and the Wasserstein metric for processes as in Barbour and Brown [Stochastic... Denzler, J, McCann, RJ Fast Diffusion to Self-Similarity: Complete Spectrum, Long-Time Asymptotics, and Numerology ARCH RATION MECH ANAL, eFirst Rockner, M, Zhang, TS Sample path large deviations for diffusion processes on configuration spaces over a Riemannian manifold PUBL RES I MATH SCI 40 (2): 385-427 JUL 2004 10 of 164 from http://isi4.isiknowledge.com/portal.cgi ------- The strong solution of the Monge-Ampere equation on the Wiener space for log-concave densities Feyel, D. / Ustunel, A.S., Comptes Rendus Mathematique, Jul 2004 ...Monge problem transporting mu to nu and realizing the H -Wasserstein distance between mu and nu . We prove that phi D 2,2 hence...Monge qui transporte mu sur nu et qui realise la distance de Wasserstein entre mu et nu par rapport a la metrique de Cameron-Martin... Chiral mixtures Michel Petitjean, Journal of Mathematical Physics, Jul 2002 ...given. Connections between chirality, Wasserstein distances, and least squares Procrustes...to colors, and an extension of the Wasserstein distance will be preferred. II. COLORED MIXTURES AND WASSERSTEIN DISTANCES The assumption that is distributed.... Michel Petitjean ITODYS (CNRS, ESA 7086), 1 rue Guy de la Brosse, 75005 Paris, France (Received 22 November 2001; accepted 11 April 2002 An index evaluating the amount of chirality of a mixture of colored random variables is defined. Properties are established. Extreme chiral mixtures are characterized and examples are given. Connections between chirality, Wasserstein distances, and least squares Procrustes methods are pointed out. ©2002 American Institute of Physics. doi:10.1063/1.1484559 PACS: 33.15.Bh, 02.50.Cw, 02.70.Rr, 02.10.Ab Geometric inequalities via a general comparison principle for interacting gases Agueh, M. / Ghoussoub, N. / Kang, X., Oct 2003 ...inequality relates the relative total energy --internal, potential and interactive -- of two arbitrary probability densities,their Wasserstein distance, their barycentres and their entropy productionfunctional. The framework is remarkably encompassing as it implies... Full text article available from E-Print ArXiv F:\Projects\ISreview\abst00-32.DVI Feb 2003 ...convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric. Key words: Discrepancy Hellinger distance Probability metrics Prokhorov metric Relative entropy Rates of convergence Wasserstein distance. [http://www.cbs.nl/isi/ISReview/abst00-32.pdf] A Diffuse Interface Approach to Hele?Shaw Flow Jan 2001 ...Hele?Shaw problem is the so?called ``Wasserstein'' metric (sometimes called the L 2 Kantorovich...transport and its relationship to the Wasserstein metric is provided. Then a diffuse interface...evolution equation and gradient flows in the Wasserstein metric is given. 2. The optimal transport... [http://www.math.utah.edu/~glasner/heleshaw.ps] Probability distance inequalities on Riemannian manifolds and path spaces Wang, F.-Y., Journal of Functional Analysis, Jan 2004 ...manifold. As an application, some new estimates are obtained for Wasserstein distances by using a Sobolev-Poincare type inequality introduced...holds on th CVGMT: Papers Oct 2004 ...distance functions for absolute minimizers (2004) A. Brancolini G. Buttazzo F. Santambrogio (Preprint) Path Functionals over Wasserstein Spaces (2004) G. Buttazzo - M. Mintchev (Preprint) Curve brachistocrone in campi di gravita' (2004) E. Berchio - F. Gazzola... [http://cvgmt.sns.it/papers/] The optimal evolution of the free energy of interacting gases and its applications Agueh, M. / Ghoussoub, N. / Kang, X., Comptes Rendus Mathematique, Aug 2003 ...interactive - energy of two arbitrary probability densities, their Wasserstein distance, their barycenters and their generalized relative...interactive - de deux densites de probabilite, leur distance de Wasserstein, leurs barycentres ainsi que leur entropie relative generalisee... Asymptotic behavior for doubly degenerate parabolic equations Agueh, M., Comptes Rendus Mathematique, Sep 2003 ...establish an exponential decay in relative entropy and in the c -Wasserstein distance of solutions - or self-similar solutions - of (1...exponentielle de la difference d'entropies et de la distance de Wasserstein - suivant le cout c - des solutions de l'equation et de sa... Carlen Abstract Eric Carlen / Georgia Tech, Oct 2000 Variational Problems in the Wasserstein metric and Kinteic Theory Eric Carlen Georgia Tech Abstract...solving a sequence of constrained variational problems in a Wasserstein metric. The constraints provide the conservation of mass... [http://icam.vt.edu/SEARCDE_2000/carlen.html] On the Initial-Value Problem in the Lifshitz--Slyozov--Wagner Theory of Ostwald Ripening Barbara Niethammer / Robert L. Pego, Apr 2004 ...topology on the space of size distributions, one given by the Wasserstein metric which measures the smallest maximum volume change...Ostwald ripening, mean-field model, measure-valued solutions, Wasserstein metric AMS Subject Classifications . 35L65, 82C21, 82C26... [http://epubs.siam.org/sam-bin/dbq/article/33821] AN00 Jun 2000 ...in Quasi Hydrodynamic Models for Charged Fluids Ingenuin Gasser, University of Hamburg, Germany 5:00-5:25 Gradient Flow in Wasserstein Metrics and the Spatially Inhomogeneous Kinetic Fokker Planck Equation Eric Carlen, Georgia Institute of Technology , USA... [http://www.siam.org/meetings/an00/MS30.htm] ESAIM: Mathematical Modelling and Numerical Analysis May 2003 ...Approximation of Parabolic Equations Using the Wasserstein Metric M2AN, Vol. 33, N 4, 1999, p...Approximation of Parabolic Equations Using the Wasserstein Metric David Kinderlehrer Department...We present formulae for computing a Wasserstein metric which enters into the variational... [http://www.edpsciences.org/articles/m2an/abs/1999/04/m...] APPROXIMATIONS OF PARABOLIC EQUATIONS BASED UPON Jan 1999 ...PARABOLIC EQUATIONS BASED UPON WASSERSTEIN'S VARIATIONAL PRINCIPLE DAVID KINDERLEHRER...present formulae for computing a Wasserstein metric which enters into the variational formulations. Key words. Wasserstein Metric, Parabolic Equations, Numerical... [http://www.math.cmu.edu/users/nw0z/publications/99-CNA...] rachetarma Oct 2001 ...13], [14], [16], [21], [22], Wasserstein metric techniques. This overcomes...naturally leads to the concept of Wasserstein distance on the space of probability measures. We recall that the Wasserstein metric is defined as follows d... [http://www.math.cmu.edu/~nw0z/publications/01-CNA-002/... ON CHOOSING AND BOUNDING PROBABILITY Feb 2002 ...relative entropy, rates of convergence, Wasserstein distance. First author supported in...distance TV Total variation distance W Wasserstein (or Kantorovich) metric 2 2 distance...L(Y ) = g (Lindvall 1992, p. 19). Wasserstein (or Kantorovich) metric. 1. State space... more hits from [http://www.math.hmc.edu/~su/papers.dir/metrics.ps]] PDE/Applied Math Seminar, University of Maryland, College Park Dec 1998 ...Robert Pego ( rlp@math.umd.edu Sept 10 Gronwall inequalities, Wasserstein metrics, measure-valued solutions, and domain coarsening...Dec 3 Special Seminar (Thursday, 2pm in room 3206 MTH) Wasserstein distance and its applications W. Gangbo, Georgia Tech, Atlanta... [http://www.math.umd.edu/~rlp/Seminar/pdeseminar98f.htm...] C:\DICICCIO\BANFF2002\ABSTRACTS\PScontributed\CHEN2.DVI May 2002 ...particular metric thereby allowing wider applicability. A Wasserstein pseudo-metric is also intro- duced for measuring the accuracy...the total variation distance for random variables and the Wasserstein metric for processes as in Barbour and Brown (1992). Also... [http://www.stat.cornell.edu/news/IMSMeeting/CHEN2.pdf] program.dvi Oct 2000 ...30 K. Howard T. Khan T. Dankel 10:30?11:00 Break 11:00?12:00 Plenary Lecture: Eric Carlen "Variational Problems in the Wasserstein metric and Kinteic Theory" 12:00? 2:00 Lunch Break 2:00? 3:00 Plenary Lecture: James Glimm "Asymptotic Analysis of Fluid... [http://icam.vt.edu/SEARCDE_2000/program.pdf] SHAPE RECOGNITION VIA WASSERSTEIN DISTANCE Wilfrid Gangbo School of Mathematics, Georgia Institute of Technology Atlanta, GA 30332, USA gangbo@math.gatech.edu Robert J. McCanny Department of Mathematics, Brown University Providence, RI 02912, USA mccann@math.brown.edu August 2, 2000 Eustasio del Barrio, Evarist Gin?, and Carlos Matr?n Central Limit Theorems for the Wasserstein Distance Between the Empirical and the True Distributions Ann. Probab. 27 (1999), no. 2, 1009?1071 Eustasio del Barrio, Evarist Gin?, and Carlos Matr?n Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions Ann. Probab. 31 (2003), no. 2, 1142?1143 Free probability analogue of the Wasserstein distance on trace state space Dan Voiculescu created Fri Feb 23 11:13:40 PST 2001 Natella O'Bryant Stability of a stochastic process on a cone-shaped Hamiltonian. Abstract: We investigate the time evolution of the laws of a stochastic process whose trajectories are governed by a two-dimensional weakly dissipative dynamical system with a cone-shaped Hamiltonian, with the critical point at the origin. Studying the Wasserstein $L_p$-distance as the shortest distance between these laws on the corresponding canonical probability spaces, we show that it is Markovian and non-expansive (up to a constant) in time. - Weak convergence of stratified processes: Wasserstein distance and Khasminskii's coordinates. Abstract: We consider laws of the graph-valued processes whose trajectories are governed by two-dimensional weakly dissipative dynamical systems with a degenerate Hamiltonian. Using a particular Wasserstein distance as the shortest distance between the measures on the corresponding canonical probability spaces, we estimate the rate of the weak convergence of the laws of the original process to the unique law of a Markov process evolving on a stratified graph. In one of our previous papers, we have computed the distance in the related classical case, and showed that the corresponding distance in the stratified case is at least of the order of the distance in the related classical case, and at most of the order delivered by the total variation of these measures over the paths crossing the boundary of the critical set of the degenerate Hamiltonian. In this work we investigate whether this total variation is connected with the gluing conditions. The analysis of the convergence of these measures relies on a finer set of so-called Khasminskii's coordinates used about the boundary of the critical set. Is it possible to obtain an explicit bound on the total variation of these laws using Khasminskii's coordinates? This question is likely to be connected to the previous one, and if answered positively, will reveal the role that gluing plays in this matter. Rate of the Weak Convergence of a Stochastic Stratified Process. Submitted. Abstract: We consider laws of a stochastic process whose trajectories are governed by a two-dimensional weakly dissipative dynamical system with a degenerate Hamiltonian. Using Wasserstein distance as the shortest distance between the measures on the corresponding canonical probability spaces, we estimate the rate of the weak convergence of the laws of the original process to the unique law of a Markov process evolving on a stratified space. Additionally, for a related (non-stratified) example of a process on a cylinder, the corresponding estimates are obtained using two different methods. One of the methods revealed the explicit expression for the Wasserstein distance. By presenting this work, we make the first explicit attempt to use minimal metrics to estimate the rate of convergence of stochastic stratified processes. CURVE IN SPAZI DI WASSERSTEIN Giuseppe Buttazzo Dipartimento di Matematica Universitµa di Pisa buttazzo@dm.unipi.it http://cvgmt.sns.it Lizzanello, 30.9 { 2.10 2004 Gradient Flows in the Wasserstein spaces of Probability Measures Giuseppe Savar ´e Department of Mathematics - University of Pavia and Institute of Applied Mathematics and Information Technology in collaboration with Luigi Ambrosio, Nicola Gigli Part of forthcoming E.T.H. Lecture Notes, Birkh¨auser http://www.imati.cnr.it/ savare, http://cvgmt.sns.it WASSERSTEIN METRIC AND LARGE TIME ASYMPTOTICS OF NONLINEAR DIFFUSION EQUATIONS J.A. CARRILLO Departament de Matem`atiques - ICREA, Universitat Aut`onoma de Barcelona, E-08193 - Bellaterra Spain E-mail: carrillo@mat.uab.es G. TOSCANI Dipartimento di Matematica, Universit´a di Pavia, 27100 Pavia Italy E-mail: toscani@dimat.unipv.it Goodness-of-fit tests for location and scale families based on a weighted L2-Wasserstein distance measure. T. de Wet Department of Statistics and Actuarial Science. University of Stellenbosch, South Africa. Contractivity of Wasserstein-type distances: asymptotic pro les, equilibration rates and qualitative properties Jos´e A. Carrillo. Asymptotics for empirical Wasserstein distances Eustasio del Barrio Department of Statistics and Operations Research, University of Valladolid, Prado de la Magdalena S/N, 47005, Valladolid, Spain [tasio@eio.uva.es] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls February 1, 2004 Luca Petrelli1 Department of Mathematical Sciences Carnegie Mellon University, Pittsburgh, PA 15213 luca@andrew.cmu.edu Gradient Flows in the Wasserstein spaces of Probability Measures Giuseppe Savar ´e Department of Mathematics - University of Pavia and Institute of Applied Mathematics and Information Technology in collaboration with Luigi Ambrosio, Nicola Gigli WASSERSTEIN METRIC AND LARGE TIME ASYMPTOTICS OF NONLINEAR DIFFUSION EQUATIONS J.A. CARRILLO Departament de Matem`atiques - ICREA, Universitat Aut`onoma de Barcelona, E-08193 - Bellaterra Spain E-mail: carrillo@mat.uab.es G. TOSCANI Dipartimento di Matematica, Universit´a di Pavia, 27100 Pavia Italy E-mail: toscani@dimat.unipv.it