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

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