Striking universalities in stochastic resetting processes

¹ Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev - Sede Boqer Campus, Sede Boqer, 8499000, Israel
² Université Paris-Saclay, CNRS, LPTMS - 91405, Orsay, France
³ Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 4 Place Jussieu, 75252 Paris Cedex 05, France

^(a) E-mail: schehr@lpthe.jussieu.fr (corresponding author)

Received: 6 April 2023
Accepted: 22 May 2023

Abstract

Given a random process which undergoes stochastic resetting at a constant rate r to a position drawn from a distribution , we consider a sequence of dynamical observables associated to the intervals between resetting events. We calculate exactly the probabilities of various events related to this sequence: that the last element is larger than all previous ones, that the sequence is monotonically increasing, etc. Remarkably, we find that these probabilities are “super-universal”, i.e., that they are independent of the particular process , the observables A_k's in question and also the resetting distribution . For some of the events in question, the universality is valid provided certain mild assumptions on the process and observables hold (e.g., mirror symmetry).