Random walks on networks with stochastic resetting

TL;DR

This paper analyzes how stochastic resetting influences random walks on various networks, providing formulas for stationary distributions and passage times, and applying these to different network structures to understand search efficiency.

Contribution

It introduces a spectral formalism for random walks with resetting on arbitrary networks, extending the analysis of resetting processes to complex network domains.

Findings

Resetting alters the stationary distribution and first passage times.

The formalism applies to diverse network types including small-world and community-structured networks.

Results improve understanding of search efficiency in network exploration.

Abstract

We study random walks with stochastic resetting to the initial position on arbitrary networks. We obtain the stationary probability distribution as well as the mean and global first passage times, which allow us to characterize the effect of resetting on the capacity of a random walker to reach a particular target or to explore a finite network. We apply the results to rings, Cayley trees, random and complex networks. Our formalism holds for undirected networks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the search efficiency in different structures with the small-world property or communities. In this way, we extend the study of resetting processes to the domain of networks.