Mixing of the symmetric beta-binomial splitting process on arbitrary graphs
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 by Morris (2006) to bound the mixing time of the exclusion process.
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