Diffusion with Stochastic Resetting

TL;DR

This paper investigates how stochastic resetting in diffusion processes creates nonequilibrium stationary states, optimizes search times, and alters survival probabilities, revealing novel effects of resetting on diffusive search dynamics.

Contribution

It introduces a model of diffusion with stochastic resetting, analyzing its stationary states, search efficiency, and survival probabilities, highlighting new effects of resetting.

Findings

Finite mean search time with an optimal resetting rate r^*

Stationary states exhibit non-Gaussian fluctuations

Altered decay of survival probability with multiple searchers

Abstract

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r^*. Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers.