The mean field Schrödinger problem: Ergodic behavior, entropy estimates and functional inequalities

Julio Backhoff-Veraguas*, Giovanni Conforti, Ivan Gentil, Christian Léonard

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
3 Downloads (Pure)

Abstract

We study the mean field Schrödinger problem (MFSP), that is the problem of finding the most likely evolution of a cloud of interacting Brownian particles conditionally on the observation of their initial and final configuration. Its rigorous formulation is in terms of an optimization problem with marginal constraints whose objective function is the large deviation rate function associated with a system of weakly dependent Brownian particles. We undertake a fine study of the dynamics of its solutions, including quantitative energy dissipation estimates yielding the exponential convergence to equilibrium as the time between observations grows larger and larger, as well as a novel class of functional inequalities involving the mean field entropic cost (i.e. the optimal value in (MFSP)). Our strategy unveils an interesting connection between forward backward stochastic differential equations and the Riemannian calculus on the space of probability measures introduced by Otto, which is of independent interest.
Original languageEnglish
Pages (from-to)475-530
JournalProbability Theory and Related Fields
Volume178
Early online date23 Jun 2020
DOIs
Publication statusPublished - Oct 2020

Keywords

  • UT-Hybrid-D

Fingerprint

Dive into the research topics of 'The mean field Schrödinger problem: Ergodic behavior, entropy estimates and functional inequalities'. Together they form a unique fingerprint.

Cite this