Cover times with stochastic resetting

TL;DR

This paper provides exact and approximate calculations of cover times for stochastic search processes with resetting, revealing how resetting influences search efficiency across various models and dimensions.

Contribution

It introduces a unified framework for computing cover times with stochastic resetting for diverse processes and geometries, including exact solutions in 1D and approximations in higher dimensions.

Findings

Exact mean cover time for 1D Brownian search with resetting

Approximate moments for cover times in higher dimensions and networks

Results applicable to a broad class of stochastic processes and resetting distributions

Abstract

Cover times quantify the speed of exhaustive search. In this work, we compute exactly the mean cover time associated with a one-dimensional Brownian search under exponentially distributed resetting. We also approximate the moments of cover times of a wide range of stochastic search processes in $d$-dimensional continuous space and on an arbitrary discrete network under frequent stochastic resetting. These results hold for a large class of resetting time distributions and search processes including diffusion and Markov jump processes.