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

This article is cited in 24 scientific papers (total in 25 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
\Bibitem{Ver04}
\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
\mathnet{http://mi.mathnet.ru/znsl773}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2117883}
\zmath{https://zbmath.org/?q=an:1090.28009}
\elib{http://elibrary.ru/item.asp?id=9129081}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 133
\issue 4
\pages 1410--1417
\crossref{https://doi.org/10.1007/s10958-006-0056-3}
\elib{http://elibrary.ru/item.asp?id=13522843}


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    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
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    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
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    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
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  • Записки научных семинаров ПОМИ
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