Stochastic Resetting and Large Deviations

TL;DR

This paper introduces stochastic resetting in diffusion processes, explores large deviation properties of related functionals, and generalizes from Poissonian to non-Poissonian resetting, highlighting its significance in statistical physics.

Contribution

It provides a comprehensive introduction to diffusion with stochastic resetting and extends the analysis to non-Poissonian resetting mechanisms.

Findings

Analysis of large deviation properties of resetting costs

Extension from Poissonian to non-Poissonian resetting processes

Insights into nonequilibrium stationary states in stochastic systems

Abstract

Stochastic resetting has been a subject of considerable interest within statistical physics, both as means of improving completion times of complex processes such as searches and as a paradigm for generating nonequilibrium stationary states. In these lecture notes we give a self-contained introduction to the toy model of diffusion with stochastic resetting. We also discuss large deviation properties of additive functionals of the process such as the cost of resetting. Finally, we consider the generalisation from Poissonian resetting, where the resetting process occurs with a constant rate, to non-Poissonian resetting.