Stochastic homogenization of dynamical discrete optimal transport

TL;DR

This paper investigates how dynamical optimal transport on random graphs behaves at large scales, establishing a stochastic homogenization result that links discrete graph problems to a continuous optimal transport framework.

Contribution

It introduces a stochastic homogenization theorem that describes the effective large-scale behavior of dynamical optimal transport on stationary random graphs.

Findings

Effective behavior characterized by a continuous optimal transport problem

Homogenized energy density depends on graph geometry

Bridges discrete and continuous optimal transport theories

Abstract

The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. 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.