Cover times with stochastic resetting.

Abstract

Cover times quantify the speed of exhaustive search. In this work, we 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 approximations apply to a large class of resetting time distributions and search processes including diffusion, run-and-tumble particles, and Markov jump processes. We illustrate these results in several examples; in the case of diffusive search, we show that the errors of our approximations vanish exponentially fast. Finally, we derive a criterion for when endowing a discrete state search process with minimal stochastic resetting reduces the mean cover time.