Striking universalities in stochastic resetting processes

Abstract

Given a random process $x(\tau )$ which undergoes stochastic resetting at a constant rate $r$ to a position drawn from a distribution $\mathcal{P}(x)$, we consider a sequence of dynamical observables $A_1,\dots ,A_n$ 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 $x(\tau )$, the observables $A_k$'s in question and also the resetting distribution $\mathcal{P}(x)$. 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).

arXiv commentMain text: 6 pages + 2 figs., Supp. Mat: 2 pages + 2 figs

References in corpus (28)

• Motility-Induced Phase Separation
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• First order transition for the optimal search time of Lévy flights with resetting
• Optimal stochastic restart renders fluctuations in first passage times universal
• Experimental realization of diffusion with stochastic resetting
• Diffusion under time-dependent resetting
• Run and tumble particle under resetting: a renewal approach
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Stochastic resetting in backtrack recovery by RNA polymerases
• Diffusion with stochastic resetting at power-law times
• Random walks with preferential relocations to places visited in the past and their application to biology
• Monotonous continuous-time random walks with drift and stochastic reset events
• The inspection paradox in stochastic resetting
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Optimization in First-Passage Resetting
• On subdiffusive continuous time random walks with stochastic resetting
• Properties of additive functionals of Brownian motion with resetting
• Long time scaling behaviour for diffusion with resetting and memory
• Continuous-time random walks with reset events: Historical background and new perspectives
• The longest excursion of stochastic processes in nonequilibrium systems
• Number of distinct sites visited by a resetting random walker
• Exact statistics of record increments of random walks and Lévy flights
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Sparre-Andersen theorem with spatiotemporal correlations
• Scaling Exponent for Incremental Records

Cited by in corpus (6)

• First detection probability in quantum resetting via random projective measurements
• Current fluctuations in stochastically resetting particle systems
• Extremal statistics for a resetting Brownian motion before its first-passage time
• Occupation time of a system of Brownian particles on the line with steplike initial condition
• Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems
• Poisson points, resetting, universality and the role of the last item