Calculus of Variations and Geometric Measure Theory

L. Monsaingeon - L. Tamanini - D. Vorotnikov

The dynamical Schrödinger problem in abstract metric spaces

created by tamanini1 on 23 Dec 2020

[BibTeX]

preprint

Inserted: 23 dec 2020
Last Updated: 23 dec 2020

Year: 2020

ArXiv: 2012.12005 PDF

Abstract:

In this paper we introduce the dynamical Schrödinger problem on abstract metric spaces, defined for a wide class of entropy and Fisher information functionals. Under very mild assumptions we prove a generic $\Gamma$-convergence result towards the geodesic problem as the noise parameter $\varepsilon\downarrow 0$. We also investigate the connection with geodesic convexity of the driving entropy, and study the dependence of the entropic cost on the parameter $\varepsilon$. Some examples and applications are discussed.