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Approximations of displacement interpolations by entropic interpolations

  • Christian Léonard (Paris Ouest University)
Felix-Klein-Hörsaal Universität Leipzig (Leipzig)

Abstract

The Schrödinger problem is an entropy minimization problem on a set of path measures with prescribed initial and final marginals. It arises from a large deviation principle for the empirical measures of large particle systems. When the dynamics of the particles is slowed down while the prescribed marginals are unchanged, a second level large deviation phenomenon occurs. This leads to a sequence, indexed by the slowdown parameter, of Schrödinger problems which Gamma-converges to a dynamical optimal transport problem. We will illustrate these limits in the setting of L2 displacement interpolations on Rd and L1 displacement interpolations on graphs and Finsler manifolds.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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