Stochastic resetting in a networked multiparticle system with correlated transitions

TL;DR

This paper introduces a solvable model of network growth with correlated stochastic resetting affecting many coupled degrees of freedom, revealing new phenomena like phase transitions and first-passage behaviors.

Contribution

It extends stochastic resetting theory to large, correlated systems, providing an exact solution for a network growth model with node deletion and resetting.

Findings

Exact full-time solution of the model

Emergence of a time-dependent percolation-like phase transition

Characterization of first-passage statistics

Abstract

The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the possibility of modeling a wide variety of realistic systems but also leads to interesting novel phenomenology not present in reset-free cases. However, most models where stochastic resetting is studied address the case of a finite number of uncorrelated variables, commonly a single one, such as the position of non-interacting random walkers. Here we overcome this limitation by framing the process of network growth with node deletion as a stochastic resetting problem where an arbitrarily large number of degrees of freedom are coupled and influence each other, both in the resetting and non-resetting (growth) events. We find the exact, full-time solution of the model, and several out-of-equilibrium properties are characterized as function of the growth and resetting rates, such as the emergence of a time-dependent percolation-like phase transition, and first-passage statistics. Coupled multiparticle systems subjected to resetting are a necessary generalization in the theory of stochastic resetting, and the model presented herein serves as an illustrative, natural and solvable example of such a generalization.