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A survey of the Schr\"odinger problem and some of its connections with optimal transport
- C. Léonard
- Mathematics
- 1 August 2013
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 also… Expand
From the Schr\"odinger problem to the Monge-Kantorovich problem
- C. Léonard
- Mathematics
- 11 November 2010
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 the… Expand
Transport Inequalities. A Survey
- N. Gozlan, C. Léonard
- Mathematics
- 1 March 2010
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 other… Expand
About the analogy between optimal transport and minimal entropy
- I. Gentil, C. Léonard, L. Ripani
- Mathematics
- 28 October 2015
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 type… Expand
An entropic interpolation problem for incompressible viscid fluids
- M. Arnaudon, A. B. Cruzeiro, C. Léonard, J. Zambrini
- Mathematics
- 7 April 2017
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 paper… Expand
On the convexity of the entropy along entropic interpolations
- C. Léonard
- Mathematics
- 4 October 2013
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 be… Expand
Minimization of the Kullback information of diffusion processes
- P. Cattiaux, C. Léonard
- Mathematics, Geography
- 1994
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 This… Expand
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A large deviation approach to optimal transport
- C. Léonard
- Mathematics
- 8 October 2007
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 a… Expand
Minimization of entropy functionals
- C. Léonard
- Mathematics, Computer Science
- ArXiv
- 7 October 2007
TLDR
Large deviations for Poisson random measures and processes with independent increments
- C. Léonard
- Mathematics
- 2000
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 in… Expand