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 epsilon-mixing time of the exclusion process on G with any feasible number of particles can be upper-bounded by CTEX ((2,G)) log(vertical bar V vertical bar/epsilon), where vertical bar V vertical bar is the number of vertices in G and T-EX (2,T-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 T-EX(2,T-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 ([14]) and developed by Oliveira ([15]) for studying the exclusion process on a graph.