First-passage statistics under stochastic resetting in bounded domains

Abstract

We investigate the first-passage problem where a diffusive searcher stochastically resets to a fixed position at a constant rate in a bounded domain. We put forward an analytical framework for this problem where the resetting rate r, the resetting position xr, the initial position x0, the domain size L, and the particle’s diffusion constant D are independent variables. From this we obtain analytical expressions for the mean-first passage time, survival probability and the first-passage time density in Laplace space in terms of the above independent variables, and closed forms in time-domain expression in some cases. For the first-passage time distributions their full-time profiles in time-domain are numerically obtained and validated by Monte Carlo simulations. We show that for the general resetting condition the first-passage process has rich nontrivial features as it combines effects from resetting and the finiteness of the domain. A phase diagram showing the regions for resetting-enhanced and -suppressed first-passages is obtained analytically. Counter-intuitively, resetting facilitates the first-passage event even if the particle resets to a position that is further away from the target than where it started. Finally, we show that averaging over resetting positions, resetting never helps the search compared to a random search, unless the resetting position is displaced from the initial position.