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arXiv · 2609.22520

A Criterion for Convergence of Diffusion Processes on Graphs

Leonid Koralov·Xiangyi Tao
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Abstract

In this paper, we consider diffusion processes on a graph. On the $i$-th edge, each process is governed by an operator of the form $D_{v_i}D^+_{u_i}$, and the behavior at the vertices is determined by the gluing conditions. The paper characterizes the weak convergence of a family of such processes to a limiting process in terms of the behavior of the scale and speed functions $u_i^n$ and $v_i^n$ and the parameters of the gluing conditions. This may be viewed as a generalization of Freidlin and Wentzell's result on the weak convergence of a family of processes on a line.

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Leonid Koralov, Xiangyi Tao. 2026-09-18. A Criterion for Convergence of Diffusion Processes on Graphs. https://arxiv.org/abs/2609.22520

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