Universal criterion for selective outcomes under stochastic resetting

• DOI: 10.48550/arxiv.2502.09127
• Publication Date: 2025-01-01
• Authors: Pal, Suvam; Dagdug, Leonardo; Ghosh, Dibakar; Boyer, Denis; Pal, Arnab
• Keywords: Chemical Physics (physics.chem-ph); Statistical Mechanics (cond-mat.stat-mech); Physics - Chemical Physics; Probability (math.PR); FOS: Mathematics; Soft Condensed Matter (cond-mat.soft); FOS: Physical sciences; Condensed Matter - Soft Condensed Matter; Condensed Matter - Statistical Mechanics; Mathematics - Probability

Resetting plays a pivotal role in optimizing the completion time of complex first passage processes with single or multiple outcomes/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 can not be said while conditioned on a particular outcome. The purpose of this letter is to derive a universal condition which reveals that two statistical metric -- 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 non-preferential outcomes. The universality of this result is demonstrated for a one dimensional diffusion process subjected to resetting with two absorbing boundaries.<br/>13 pages, 4 figures<br/>