  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 $\varepsilon$-mixing time of the exclusion process on
$G$ with any feasible number of particles can be upper-bounded by
$CT_{\text{EX}(2,G)}\log(|V|/\varepsilon)$, where $|V|$ is the number of
vertices in $G$ and $T_{\text{EX}(2,G)}$ 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 $T_{\mathrm{EX}(2,G)}$ 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 and developed by Oliveira for studying the
exclusion process on a graph.
