Sampling rare fluctuations of discrete-time Markov chains

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• Discrete-time Markov chains are fundamental in modeling stochastic processes.
• Understanding rare fluctuations is crucial for predicting system behavior and stability.
• Active matter systems exhibit complex emergent behaviors like phase separation.

Purpose of the Study:

• To develop a simple and efficient method for sampling rare fluctuations in discrete-time Markov chains.
• To derive large-deviation rate functions for dynamical quantities in Markov chains.
• To apply the developed method to study fluctuations in active matter models.

Main Methods:

• Derivation of expressions for large-deviation rate functions.
• Focus on Markov chains with well-defined steady-state measures.
• Application to a lattice-based model of active matter.

Main Results:

• A straightforward method for sampling rare fluctuations is presented.
• Expressions for large-deviation rate functions and their upper bounds are derived.
• The method successfully studied fluctuations in a motility-induced phase separation model.

Conclusions:

• The proposed method provides an effective tool for analyzing rare events in Markovian systems.
• This approach facilitates the study of complex phenomena like phase separation in active matter.
• The findings contribute to a deeper understanding of stochastic processes and their applications.