Stochastic resetting in a networked multiparticle system with correlated transitions

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.

Preface: stochastic resetting—theory and applications

“…Additional contributors to this special issue have also delved into the influence of stochastic resetting on interacting systems. Artime framed the problem of network growth with node deletion as a stochastic resetting problem [65]. He finds an exact solution for the time-dependent degree distribution, calculates the first passage time to a fixed degree threshold, and demonstrates the emergence of a time-dependent percolation-like phase transition.…”