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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2604.20984 |
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| _version_ | 1866917430344810496 |
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| author | Zhang, Edith J. Scott, James Du, Qiang |
| author_facet | Zhang, Edith J. Scott, James Du, Qiang |
| contents | A graph reaction--diffusion (RD) equation is a system of differential equations that is defined on the nodes of a graph. Consider a sequence of growing graphs that converges in cut norm to a limiting graphon. We show that the solutions of the sequence of graph RD equations converge in $L^p$ norm, for $p \in [1,\infty]$, to the solution of a limiting nonlocal RD equation, which we call a graphon RD equation. Furthermore, we show a large numbers result for a stochastic particle process that consists of a random walk and a birth-death process on graphs. For a sequence of graphs that converge in cut norm to a limiting graphon, the sequence of stochastic processes converges in probability to the solution of the graphon RD equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20984 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Graphon Limits of Graph Reaction--Diffusion Equations Zhang, Edith J. Scott, James Du, Qiang Dynamical Systems Probability 37A50, 35K57, 05C63 A graph reaction--diffusion (RD) equation is a system of differential equations that is defined on the nodes of a graph. Consider a sequence of growing graphs that converges in cut norm to a limiting graphon. We show that the solutions of the sequence of graph RD equations converge in $L^p$ norm, for $p \in [1,\infty]$, to the solution of a limiting nonlocal RD equation, which we call a graphon RD equation. Furthermore, we show a large numbers result for a stochastic particle process that consists of a random walk and a birth-death process on graphs. For a sequence of graphs that converge in cut norm to a limiting graphon, the sequence of stochastic processes converges in probability to the solution of the graphon RD equation. |
| title | Graphon Limits of Graph Reaction--Diffusion Equations |
| topic | Dynamical Systems Probability 37A50, 35K57, 05C63 |
| url | https://arxiv.org/abs/2604.20984 |