We describe a simple method that can be used to sample the rare fluctuations
of discrete-time Markov chains. We focus on the case of Markov chains with
well-defined steady-state measures, and derive expressions for the
large-deviation rate functions (and upper bounds on such functions) for
dynamical quantities extensive in the length of the Markov chain. We illustrate
the method using a series of simple examples, and use it to study the
fluctuations of a lattice-based model of active matter that can undergo
motility-induced phase separation.Comment: Submitted along with arXiv:1709.03951 as a joint wor
