Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Koralov, Leonid, Tao, Xiangyi
Institution: University of Maryland, College Park
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214046344
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