L.N.Vaserstein, Markov  processes on product of spaces,

1965 Moscow State University Price for undergraduate research.


Markov processes on countable space products describing large systems 

 of   automata, 

Probl.Pered.Inform. 5:3 (1969), 64-72 = Probl. Inform.Transm. 5:3, 47-52. 

MR0314115 (47 #2667)   Z273.60054. RZh 1970.2V388.    2.24.69. 

Cited in 29 publications in Math Reviews including  51 #7055    |  50 #1326  |  48 #7324   |  

Wasserstein distance:  

217 reviews with Vaserstein  in review text from Math Reviews 

141 references in MR 

85 results    from ISI Web of Knowledge with Wasserstein in topic    

 298 results  from Web of Science  with Wasserstein in topic.

to be updated

See also Wasserstein Wasershtein Vasershtein  Vasserstein Vaserstein

My name in books

My name in title from Math Reviews

My name in title from other sources

MR1784174 (2002b:60055)  Mikami, T.(J-HOKK) Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric. (English summary) 

Appl. Math. Optim. 42 (2000), no. 2, 203–227.   60F15 (60H30 82C35)

Path Functionals over Wasserstein Spaces  Preprint (2004)  

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 

Print ISSN: 1532-6349

Online ISSN: 1532-4214

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)

Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls February 1, 2004 Luca Petrelli 1 Department of Mathematical ...

Contractivity of Wasserstein-type distances:

asymptotic profiles, equilibration rates and qualitative properties.

Carrillo in collaboration with R. J. McCann, C. Villani1; G. Toscani. Paris 2004


math.OA/0006044 [abs, ps, pdf, other] :

    Title: A Free Probability Analogue of the Wasserstein Metric on the Trace-State Space

    Authors: Philippe Biane, Dan Voiculescu

    Comments: 14 pages, Incomplete Preliminary Version

    Subj-class: Operator Algebras

MSC-class: 46L54; 60E99; 94A17

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

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)

 MR0328982 (48 #7324) Vallander, S. S. Calculations of the Vasser\v ste\u\i n distance between probability distributions on the line. (Russian) Teor. Verojatnost. i Primenen. 18 (1973), 824--827. (Reviewer: I. Csiszar) 60B05


kotecky | malyshev  | 


 Pestov, see e-mail |

Vladimir Pestov <vova@mcs.vuw.ac.nz>

Re: distance

April 9, 2002 4:57 PM

Maybe you would be interested to know that topological algebraists have

discovered the distances of this type back in the 50s, it was done by

Graev (on free / free abelian groups on metric spaces) and Arens-Eells

(on linear spaces having a given metric space as the Hamel basis). 

Graev, M. I.Free topological groups. (Russian)

 Izvestiya Akad. Nauk SSSR. Ser. Mat. 12, (1948). 279--324.


Arens, Richard F.; Eells, James, Jr.

On embedding uniform and topological spaces.

Pacific J. Math. 6 (1956), 397--403.



Breugel see e-mail | 

Hutchinson metric - Wikipedia, the free encyclopedia

MR0625600  Hutchinson, John E. Fractals and self-similarity. Indiana Univ. Math. J. 30 (1981), no. 5, 713–747. (Reviewer: F. J. Almgren Jr.) 49F20 (00A69 28A12 58C27). Hutchinson.pdf

Franck van Breugel <franck@cs.yorku.ca>

Wasserstein metric

December 16, 2003 2:54 PM

Hutchinson independently came up with a similar distance

function in his paper

 Fractals and self similarity.

 Indiana University Mathematics Journal, 30(5):713--747, 1981.

The metric is sometimes called the Hutchinson metric (for example,

in the book Fractals Everywhere by Michael Barnsley).

Franck van Breugel

MR1460463 (99e:28011) Åkerlund-Biström, Cecilia 

A generalization of the Hutchinson distance and applications.  

Random Comput. Dynam.  5  (1997),  no. 2-3, 159--176. (Reviewer: S. Dubuc) 28A80 (58F12)


MR1345798 (96g:60005) Barahona, Francisco; Cabrelli, Carlos A.; Molter, Ursula M. Matching probability measures on the line under translation. Random Comput. Dynam. 3 (1995), no. 3, 121--135. 60B05 (65U05)

MR1181383 Barahona, Francisco; Cabrelli, Carlos A.; Molter, Ursula M. Computing the Hutchinson distance by network flows. Random Comput. Dynam. 1 (1992/93), no. 1, 117--129. 90B15

MR1143907 Brandt, Jonathan; Cabrelli, Carlos; Molter, Ursula An algorithm for the computation of the Hutchinson distance. Inform. Process. Lett. 40 (1991), no. 2, 113--117. 68Q25

 Hutchinson J., "Fractals and self similarity," Indiana Univ. Math. J., 30, No. 5, 713--747 (1981). MR0625600 (82h:49026)



Encyclopedia of Distances - Page 51, 147, 253, 254, 571, 580, 590

Michel M. Deza, Elena Deza - Springer 2009 - 590 pages ISBN 364200234X, 9783642002342

fLip≤1 ∫ If μ and ν are probability measures, then it is the Kantorovich–Mallows–Monge-Wasserstein metric (cf. Chap. 14).

from SPIN:

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.


PACS: 33.15.Bh, 02.50.Cw, 02.70.Rr, 02.10.Ab   

Earth mover's distance - Wikipedia, the free encyclopedia

In computer science, the earth mover's distance (EMD) is a measure of the distance between two probability distributions over a region D. In mathematics, this is known as the Wasserstein metric. Informally, if the distributions are interpreted as two different ways of piling up a certain amount of dirt over the region D, the EMD is the minimum cost of turning one pile into the other; where the cost is assumed to be amount of dirt moved times the distance by which it is moved.[1]