Sampling rare fluctuations of discrete-time Markov chains
arXiv:1709.03953 · doi:10.1103/PhysRevE.97.032122
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.
Submitted along with arXiv:1709.03951 as a joint work
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- Phase separation and large deviations of lattice active matter
- Dissipation controls transport and phase transitions in active fluids: Mobility, diffusion and biased ensembles
- Large deviations in the presence of cooperativity and slow dynamics
- Direct evaluation of dynamical large-deviation rate functions using a variational ansatz
- Target search of active agents crossing high energy barriers
- Large deviations in models of growing clusters with symmetry-breaking transitions
- Efficient large deviation estimation based on importance sampling
- Multi-point nonequilibrium umbrella sampling and associated fluctuation relations