Global resetting and emergent correlations: exit statistics in an interval
File(s)
Published version
Author(s)
Bressloff, Paul C
Type
Journal Article
Abstract
There is considerable current interest in the emergence of statistical correlations within a population of otherwise non-interacting Brownian particles subject to a common fluctuating environment or drive. Examples include global stochastic resetting, switching confining potentials, fluc
tuating diffusivities, and stochastically gated boundaries. Most studies have focused on the analytical structure of the stationary joint probability density (assuming it exists). In this paper, we extend previous work on the exit statistics of multiple particles in stochastically gated domains to the case of global resetting in an interval with absorbing boundaries at both ends. First, we use a generalised Itˆo’s lemma to derive a hierarchy of boundary value problems (BVPs) for the joint splitting probability that all particles exit from the same end of the interval. The BVPs form a nested sequence with respect to the initial number of particles M. We explicitly solve the BVP for a pair of particles (M = 2) and use this to illustrate the emergence of pairwise correlations. Second, we show how the BVP for the splitting probability of M Brownian particles can be mapped onto the Mth order moment equation of a stochastic diffusion equation with resetting. We thus
establish a general mathematical framework to study exit problems for globally-driven particle systems.
tuating diffusivities, and stochastically gated boundaries. Most studies have focused on the analytical structure of the stationary joint probability density (assuming it exists). In this paper, we extend previous work on the exit statistics of multiple particles in stochastically gated domains to the case of global resetting in an interval with absorbing boundaries at both ends. First, we use a generalised Itˆo’s lemma to derive a hierarchy of boundary value problems (BVPs) for the joint splitting probability that all particles exit from the same end of the interval. The BVPs form a nested sequence with respect to the initial number of particles M. We explicitly solve the BVP for a pair of particles (M = 2) and use this to illustrate the emergence of pairwise correlations. Second, we show how the BVP for the splitting probability of M Brownian particles can be mapped onto the Mth order moment equation of a stochastic diffusion equation with resetting. We thus
establish a general mathematical framework to study exit problems for globally-driven particle systems.
Date Issued
2026-08-07
Date Acceptance
2026-07-23
Citation
Journal of Physics A: Mathematical and Theoretical, 2026, 59 (31)
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Volume
59
Issue
31
Copyright Statement
© 2026 The Author(s). Published by IOP Publishing Ltd Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
License URL
Publication Status
Published
Date Publish Online
2026-08-06