A formula for the time derivative of the entropic cost and applications

In the recent years the Schrödinger problem has gained a lot of attention because of the connection, in the small-noise regime, with the Monge-Kantorovich optimal transport problem. Its optimal value, the entropic costCT, is here deeply investigated. In this paper we study the regularity of CT with...

Full description

Saved in:
Bibliographic Details
Published inJournal of functional analysis Vol. 280; no. 11; p. 108964
Main Authors Conforti, Giovanni, Tamanini, Luca
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2021
Subjects
Entropic cost
Optimal transport
Schrödinger problem
Short- and long-time behavior
Schrödinger problem
Entropic cost
Optimal transport
Short- and long-time behavior
Online AccessGet full text

Cover

More Information
Summary:In the recent years the Schrödinger problem has gained a lot of attention because of the connection, in the small-noise regime, with the Monge-Kantorovich optimal transport problem. Its optimal value, the entropic costCT, is here deeply investigated. In this paper we study the regularity of CT with respect to the parameter T under a curvature condition and explicitly compute its first and second derivative. As applications:-we determine the large-time limit of CT and provide sharp exponential convergence rates; we obtain this result not only for the classical Schrödinger problem but also for the recently introduced Mean Field Schrödinger problem [3];-we improve the Taylor expansion of T↦TCT around T=0 from the first to the second order.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2021.108964