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A survey of the Schr\"odinger problem and some of its connections with optimal transport
This article is aimed at presenting the Schr\"odinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schr\"odinger problem. We alsoExpand
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From the Schr\"odinger problem to the Monge-Kantorovich problem
The aim of this article is to show that the Monge-Kantorovich problem is the limit of a sequence of entropy minimization problems when a fluctuation parameter tends down to zero. We prove theExpand
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Transport Inequalities. A Survey
This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch their links with otherExpand
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About the analogy between optimal transport and minimal entropy
We describe some analogy between optimal transport and the Schr\"odinger problem where the transport cost is replaced by an entropic cost with a reference path measure. A dual Kantorovich typeExpand
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An entropic interpolation problem for incompressible viscid fluids
In view of studying incompressible inviscid fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of inviscid fluids, the present paperExpand
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On the convexity of the entropy along entropic interpolations
Convexity properties of the entropy along displacement interpolations are crucial in the Lott-Sturm-Villani theory of lower bounded curvature of geodesic measure spaces. As discrete spaces fail to beExpand
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Minimization of the Kullback information of diffusion processes
In this paper we compute an explicit expression for the rate function of large deviations for the measure valued empirical process where the Xi’s are independent copies of a diffusion process in ThisExpand
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A large deviation approach to optimal transport
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys aExpand
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Minimization of entropy functionals
  • C. Léonard
  • Mathematics, Computer Science
  • ArXiv
  • 7 October 2007
TLDR
This paper is aimed at reducing as much as possible the assumptions on the constraint set. Expand
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Large deviations for Poisson random measures and processes with independent increments
Large deviation principles are proved for rescaled Poisson random measures. As a consequence, Freidlin-Wentzell type large deviations results for processes with independent increments are obtained inExpand
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