Stochastic Resetting and Applications

Martin R. Evans, Satya N. Majumdar, Gregory Schehr

Research output: Contribution to journalArticlepeer-review

Abstract

In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. L\'evy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field.
Original languageEnglish
Number of pages68
JournalJournal of Physics A: Mathematical and Theoretical
Volume53
Issue number19
DOIs
Publication statusPublished - 20 Apr 2020

Keywords

  • cond-mat.stat-mech

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