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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 DviD+ui, 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 uin and vin 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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Cite

BibTeXRIS
BibTeX
@misc{koralov2026criterion,
  title = {{A Criterion for Convergence of Diffusion Processes on Graphs}},
  author = {Leonid Koralov and Xiangyi Tao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22520},
  eprint = {2609.22520},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22520},
}
RIS
TY  - UNPB
TI  - A Criterion for Convergence of Diffusion Processes on Graphs
AU  - Leonid Koralov
AU  - Xiangyi Tao
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.22520
UR  - https://arxiv.org/abs/2609.22520
AB  - 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_iD^+_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.
ER  -