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Zap. Nauchn. Sem. POMI, 2004, Volume 312, Pages 69–85 (Mi znsl773)  

This article is cited in 25 scientific papers (total in 26 papers)

The Kantorovich metric: initial history and little-known applications

A. M. Vershik

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We remind of the history of the transportation metric (Kantorovich metric) and the Monge–Kantorovich problem. We describe several little-known applications: the first one concerns the theory of decreasing sequences of partitions (tower of measures and iterated metric), the second one concerns Ornstein's theory of Bernoulli automorphisms ($\bar d$-metric), and the third one is the formulation of the strong Monge–Kantorovich problem in terms of matrix distributions.

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English version:
Journal of Mathematical Sciences (New York), 2006, 133:4, 1410–1417

Bibliographic databases:

UDC: 517.987
Received: 25.08.2004

Citation: A. M. Vershik, “The Kantorovich metric: initial history and little-known applications”, Representation theory, dynamical systems. Part XI, Special issue, Zap. Nauchn. Sem. POMI, 312, POMI, St. Petersburg, 2004, 69–85; J. Math. Sci. (N. Y.), 133:4 (2006), 1410–1417

Citation in format AMSBIB
\by A.~M.~Vershik
\paper The Kantorovich metric: initial history and little-known applications
\inbook Representation theory, dynamical systems. Part~XI
\bookinfo Special issue
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 312
\pages 69--85
\publ POMI
\publaddr St.~Petersburg
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 133
\issue 4
\pages 1410--1417

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    1. A. M. Vershik, A. D. Gorbul'skii, “Scaled entropy of filtrations of $\sigma$-fields”, Theory Probab. Appl., 52:3 (2008), 493–508  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Baba A., Komatsuzaki T., “Construction of effective free energy landscape from single-molecule time series”, Proceedings of the National Academy of Sciences of the United States of America, 104:49 (2007), 19297–19302  crossref  adsnasa  isi  scopus
    3. Melleray J., Petrov F.V., Vershik A.M., “Linearly rigid metric spaces and the embedding problem”, Fundamenta Mathematicae, 199:2 (2008), 177–194  crossref  mathscinet  zmath  isi  elib  scopus
    4. Laurent S., “Further comments on the representation problem for stationary processes”, Statistics & Probability Letters, 80:7–8 (2010), 592–596  crossref  mathscinet  zmath  isi  scopus
    5. Theory Probab. Appl., 55:1 (2011), 54–76  mathnet  crossref  crossref  mathscinet  isi
    6. Schuetz Ph., Wuttke R., Schuler B., Caflisch A., “Free Energy Surfaces from Single-Distance Information”, The Journal of Physical Chemistry B, 114:46 (2010), 15227–15235  crossref  isi  scopus
    7. Rigoberto Gabriel J., Gonzalez-Hernandez J., Lopez-Martinez R.R., “Numerical approximations to the mass transfer problem on compact spaces”, IMA J Numer Anal, 30:4 (2010), 1121–1136  crossref  mathscinet  zmath  isi  scopus
    8. Thorsley D., Klavins E., “Approximating stochastic biochemical processes with Wasserstein pseudometrics”, Iet Systems Biology, 4:3 (2010), 193–211  crossref  isi  elib  scopus
    9. Kaijser T., “On Markov Chains Induced by Partitioned Transition Probability Matrices”, Acta Math Sin (Engl Ser ), 27:3 (2011), 441–476  crossref  mathscinet  zmath  isi  scopus
    10. Baba A., Komatsuzaki T., “Extracting the underlying effective free energy landscape from single-molecule time series-local equilibrium states and their network”, Physical Chemistry Chemical Physics, 13:4 (2011), 1395–1406  crossref  mathscinet  isi  scopus
    11. Bogachev L.V., Zarbaliev S.M., “Universality of the Limit Shape of Convex Lattice Polygonal Lines”, Ann Probab, 39:6 (2011), 2271–2317  crossref  mathscinet  zmath  isi  elib  scopus
    12. MacKay R.S., “Robustness of Markov processes on large networks”, J Differ Equations Appl, 17:8 (2011), 1155–1167  crossref  mathscinet  zmath  isi  elib  scopus
    13. V. I. Bogachev, A. V. Kolesnikov, “The Monge–Kantorovich problem: achievements, connections, and perspectives”, Russian Math. Surveys, 67:5 (2012), 785–890  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. B. V. Oliynyk, V. I. Sushchanskiǐ, “The isometry groups of the Hamming spaces of periodic sequences”, Siberian Math. J., 54:1 (2013), 124–136  mathnet  crossref  mathscinet  isi
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    16. Vershik A.M., “Long History of the Monge-Kantorovich Transportation Problem”, Math. Intell., 35:4 (2013), 1–9  crossref  mathscinet  zmath  isi  scopus
    17. V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Russian Math. Surveys, 69:1 (2014), 165–179  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. B. V. Oliynyk, V. I. Sushchanskiǐ, “Imprimitivity systems and lattices of normal subgroups in $D$-hyperoctahedral groups”, Siberian Math. J., 55:1 (2014), 132–141  mathnet  crossref  mathscinet  isi
    19. J. Math. Sci. (N. Y.), 215:6 (2016), 649–658  mathnet  crossref  mathscinet
    20. D. A. Zaev, “On ergodic decompositions related to the Kantorovich problem”, J. Math. Sci. (N. Y.), 216:1 (2016), 65–83  mathnet  crossref  mathscinet
    21. Viktoriya L. Kreps, “Modeli birzhevykh torgov i povtoryayuschiesya igry s nepolnoi informatsiei: obzor”, MTIP, 9:3 (2017), 3–35  mathnet
    22. Wolansky G., “From Optimal Transportation to Optimal Teleportation”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 34:7 (2017), 1669–1685  crossref  mathscinet  zmath  isi  scopus
    23. V. I. Bogachev, A. N. Kalinin, S. N. Popova, “On the equality of values in the Monge and Kantorovich problems”, J. Math. Sci. (N. Y.), 238:4 (2019), 377–389  mathnet  crossref  mathscinet  zmath
    24. Austin T., “Measure Concentration and the Weak Pinsker Property”, Publ. Math. IHES, 128:1 (2018), 1–119  crossref  mathscinet  zmath  isi  scopus
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    26. Ostrovska S. Ostrovskii M.I., “Generalized Transportation Cost Spaces”, Mediterr. J. Math., 16:6 (2019), 157  crossref  mathscinet  zmath  isi
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