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arXiv · 1709.03953

Sampling rare fluctuations of discrete-time Markov chains

Stephen Whitelam
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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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Stephen Whitelam. 2018-03-11. Sampling rare fluctuations of discrete-time Markov chains. https://doi.org/10.1103/physreve.97.032122

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