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 from a cell formula.
Stochastic homogenization of dynamical discrete optimal transport
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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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Stochastic homogenisation of nonlinear minimum-cost flow problems
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 from a cell formula.