Mixing of the symmetric beta-binomial splitting process on arbitrary graphs

2023/07/05 by Richard Pymar, Pymar, Richard, Nicolás Rivera +1
Mathematics · #37A25 #60J27 #60K35 #82C22 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2307.02406

openalex publication_date 2023/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the mixing time of the symmetric beta-binomial splitting process on finite weighted connected graphs G=(V,E,\r_e\_{e∈ E}) with vertex set V, edge set E and positive edge-weights r_e>0 for e∈ E. This is an interacting particle system with a fixed number of particles that updates through vertex-pairwise interactions which redistribute particles. We show that the mixing time of this process can be upper-bounded in terms of the maximal expected meeting time of two independent random walks on G. Our techniques involve using a process similar to the chameleon process invented by Morris (2006) to bound the mixing time of the exclusion process.

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