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

Pymar, Richard and Rivera, N. (2024) Mixing of the symmetric beta-binomial splitting process on arbitrary graphs. Annales de l'Institut Henri Poincare (B) Probability and Statistics , ISSN 0246-0203. (In Press)

Abstract

We study the mixing time of the symmetric beta-binomial splitting process on finite weighted connected graphs G = (V,E,{re}e∈E) with vertex set V , edge set E and positive edge-weights re > 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 in [18] to bound the mixing time of the exclusion process.

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