A diffusion approximation for systems with frequent weak resetting

TL;DR

This paper introduces a diffusion approximation for systems experiencing frequent, small resets, enabling analysis of their stationary behavior, first-passage times, and pattern formation, with applications to multi-particle systems.

Contribution

The authors develop a novel diffusion approximation for systems with frequent weak resets, extending understanding of their stationary and dynamic properties.

Findings

Accurately computes stationary distributions and mean first-passage times.

Captures correlations in multi-particle systems with resets.

Shows resetting can induce cycles and patterns.

Abstract

We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing the stationary distribution and mean first-passage times of simple one-dimensional systems. The approximation captures dynamically induced correlations in multi-particle systems, and it can be used to generalise the conditionally independent and identically distributed structure recently found in systems with full resetting. Finally, we show that resetting can induce cycles and patterns, which can be characterised using the diffusion approximation.