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    Universal criterion for selective outcomes under stochastic resetting

    Suvam Pal1,*, Leonardo Dagdug2,†, Dibakar Ghosh1,‡, Denis Boyer3,§, and Arnab Pal4,5,∥

    • *Contact author: suvamjoy256@gmail.com
    • †Contact author: dll@xanum.uam.mx
    • ‡Contact author: dibakar@isical.ac.in
    • §Contact author: boyer@fisica.unam.mx
    • ∥Contact author: arnabpal@imsc.res.in

    Phys. Rev. E 112, 034116 – Published 5 September, 2025

    DOI: https://doi.org/10.1103/p3yc-kmt1

    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.

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