Universal criterion for selective outcomes under stochastic resetting.

Abstract

Resetting plays a pivotal role in optimizing the completion time of complex first-passage processes with single or multiple outcomes and exit possibilities. While it is well established that the coefficient of variation-a statistical dispersion defined as a ratio of the fluctuations over the mean of the first-passage time-must be larger than unity for resetting to be beneficial for any outcome averaged over all the possibilities, the same cannot be said while conditioned on a particular outcome. The purpose of this article is to derive a universal condition that reveals that two statistical metrics-the mean and coefficient of variation of the conditional times-come together to determine when resetting can expedite the completion of a selective outcome, and furthermore can govern the biasing between preferential and nonpreferential outcomes. The universality of this result is demonstrated for a one-dimensional diffusion process subjected to resetting with two absorbing boundaries.