Stochastic homogenization of dynamical discrete optimal transport

Abstract

The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in ${\mathbb{R}}^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective behavior of the discrete problems in terms of a continuous optimal transport problem, where the homogenized energy density results from the geometry of the discrete graph.

References in corpus (3)

• Recent progress on the Random Conductance Model
• Ricci curvature of finite Markov chains via convexity of the entropy
• Gradient flow structure for McKean-Vlasov equations on discrete spaces