Mixing times for exclusion processes on hypergraphs

We introduce a natural extension of the exclusion process to hypergraphs and prove an upper bound for its mixing time. In particular we show the existence of a constant C such that for any connected, regular hypergraph G within some natural class, the ε-mixing time of the exclusion process on G with any feasible number of particles can be upper-bounded by C TEX(2,G) log(|V|/ε), where |V| is the number of vertices in G and TEX(2,G) is the 1/4-mixing time of the corresponding exclusion process with just two particles. Moreover we show this is optimal in the sense that there exist hypergraphs in the same class for which TEX(2,G) and the mixing time of just one particle are not comparable. The proofs involve an adaptation of the chameleon process, a technical tool invented by Morris (2006) and developed by Oliveira (2013) for studying the exclusion process on a graph.