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Publications Influence

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

190 21- PDF

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

112 17- PDF

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

125 11- PDF

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

40 5- PDF

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

13 5- PDF

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

24 5- PDF

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

62 4- PDF

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

18 4- PDF

Minimization of entropy functionals

- C. Léonard
- Mathematics, Computer Science
- ArXiv
- 7 October 2007

TLDR

23 3- PDF

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

18 3