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 Theory Stoch. Process.: Year: Volume: Issue: Page: Find

 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}