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Theory Stoch. Process., 2015, Volume 20(36), Issue 2, Pages 54–62 (Mi thsp102)  

Exchangeable optimal transportation and log-concavity

Alexander V. Kolesnikov, Danila A. Zaev

Higher School of Economics, Moscow, Russia

Abstract: We study the Monge and Kantorovich transportation problems on $\mathbb{R}^{\infty}$ within the class of exchangeable measures. With the help of the de Finetti decomposition theorem the problem is reduced to an unconstrained optimal transportation problem on a Hilbert space. We find sufficient conditions for convergence of finite-dimensional approximations to the Monge solution. The result holds, in particular, under certain analytical assumptions involving log-concavity of the target measure. As a by-product we obtain the following result: any uniformly log-concave exchangeable sequence of random variables is i.i.d.

Keywords: Optimal transportation, log-concave measures, exchangeable measures, de Finetti theorem, Caffarelli contraction theorem.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00237
Deutsche Forschungsgemeinschaft CRC 701
National Research University Higher School of Economics 14-01-0056


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Bibliographic databases:
MSC: Primary 28C20, 90C08; Secondary 35J96
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Citation: Alexander V. Kolesnikov, Danila A. Zaev, “Exchangeable optimal transportation and log-concavity”, Theory Stoch. Process., 20(36):2 (2015), 54–62

Citation in format AMSBIB
\Bibitem{KolZae15}
\by Alexander~V.~Kolesnikov, Danila~A.~Zaev
\paper Exchangeable optimal transportation and log-concavity
\jour Theory Stoch. Process.
\yr 2015
\vol 20(36)
\issue 2
\pages 54--62
\mathnet{http://mi.mathnet.ru/thsp102}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3510228}
\zmath{https://zbmath.org/?q=an:1363.28020}


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