A kinetic model approximation of Walsh's spider process on the infinite star-like graph

2024/09/23 by Adam Bobrowski, Bobrowski, Adam, Elżbieta Ratajczyk +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Diffusion and Search Dynamics #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2409.15467

openalex publication_date 2024/09/23 · openalex created_date 2024/10/26 · openalex updated_date 2026/07/28

Abstract

We consider processes of deterministic motions on k copies of the star-like graph S_k= K_1,k with k edges which are perturbed by two stochastic mechanisms: one caused by interfaces located at the graphs' centers, the other describing jumps between different copies of the same edge. We prove that diffusing scaling of these processes leads in the limit to the Walsh's spider process on S_k.

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