Sampling rare fluctuations of discrete-time Markov chains

Physical Review. E
Stephen Whitelam

Abstract

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.

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Citations

Apr 24, 2018·The Journal of Chemical Physics·Stephen WhitelamDibyendu Mandal
Jul 18, 2018·Physical Review. E·Stephen Whitelam
Dec 25, 2019·Physical Review. E·Daniel Jacobson, Stephen Whitelam
Jan 23, 2021·Physical Review Letters·Luigi ZanovelloPietro Faccioli

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