Geodesic
Exchangeable optimal transportation and log-concavity
Teoriâ slučajnyh processov, Tome 20 (2015) no. 2, pp. 54-62

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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: log-concave measures, exchangeable measures, de Finetti theorem, Caffarelli contraction theorem.
Mots-clés : Optimal transportation 
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     title = {Exchangeable optimal transportation and log-concavity},
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Alexander V. Kolesnikov; Danila A. Zaev. Exchangeable optimal transportation and log-concavity. Teoriâ slučajnyh processov, Tome 20 (2015) no. 2, pp. 54-62. http://geodesic.mathdoc.fr/item/THSP_2015_20_2_a3/