Density-dependent stochastic resetting: a large deviations framework for achieving target distributions over networks

TL;DR

This paper introduces a large deviations framework for designing density-dependent stochastic resetting protocols to control the distribution of random walkers on networks, enabling targeted and rare configuration achievement.

Contribution

It develops a novel theoretical framework that incorporates local density-dependent resetting to influence walker distributions on networks, including transient and stationary states.

Findings

Protocols can maximize the likelihood of homogeneous distributions.

Framework captures both transient and stationary behaviors.

Enables control over rare configurations of walkers.

Abstract

We develop a framework for designing density-dependent stochastic resetting protocols to regulate distributions of random walkers on networks. Resetting mechanisms that depend on local densities induce correlations in otherwise non-interacting walkers. Our framework allows for the study of both transient trajectories and stationary properties and identifies resetting protocols that maximise the likelihood of homogeneous and, more generally, rare configurations of random walkers.