Restricted permutations for the simple exclusion process in discrete time over graphs

J. Ricardo G. Mendonça

Published 2018-06-24Version 1

Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a continuous-time stochastic process, but in many situations it would be desirable to have a discrete-time version of them. There is no generally applicable formalism for exclusion processes in discrete-time. In this paper we define the symmetric simple exclusion process in discrete time over graphs by means of restricted permutations over the labels of the vertices of the graphs and describe a straightforward sequential importance sampling algorithm to simulate the process. We investigate the approach to stationarity of the process over loop-augmented Bollob\'as-Chung "cycle-with-matches" graphs. In all cases the approach is algebraic with an exponent varying between $1$ and $2$ depending on the number of matches.