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Stochastic homogenization of dynamical discrete optimal transport

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arxiv 2411.04157 v3 pith:CCYV5KJE submitted 2024-11-06 math.PR

Peter Gladbach , Eva Kopfer This is my paper · ORCID
classification math.PR
keywords discreteoptimaltransportbehaviordynamicalhomogenizationstochasticcharacterizes
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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.

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  1. Stochastic homogenisation of nonlinear minimum-cost flow problems

    math.AP 2024-12 accept novelty 7.0 of 10

    On stationary random graphs satisfying quantitative connectedness, nonlinear minimum-cost flow problems Gamma-converge under rescaling to a continuum divergence-constrained problem with a homogenised energy density fr...

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