Diffusive limit of random walks on tessellations via generalized gradient flows

TL;DR

This paper investigates how reversible random walks on tessellations converge to diffusion processes using a variational approach based on generalized gradient flows, providing conditions for this convergence.

Contribution

It introduces a variational framework for analyzing the diffusive limits of random walks on tessellations, extending understanding of their asymptotic behavior.

Findings

Established conditions for convergence to diffusion processes

Derived a generalized-gradient-flow formulation of the Kolmogorov equation

Showed the diffusion tensor can be spatially dependent

Abstract

We study asymptotic limits of reversible random walks on tessellations via a variational approach, which relies on a specific generalized-gradient-flow formulation of the corresponding forward Kolmogorov equation. We establish sufficient conditions on sequences of tessellations and jump intensities under which a sequence of random walks converges to a diffusion process with a possibly spatially-dependent diffusion tensor.