Random walks on complex networks under node-dependent stochastic resetting

TL;DR

This paper investigates how node-dependent stochastic resetting influences random walks on complex networks, deriving exact formulas for stationary states and mean first passage times, and demonstrating potential efficiency improvements in network search tasks.

Contribution

It introduces a renewal approach to derive exact stationary and first passage metrics for node-dependent resetting, enhancing understanding of search optimization in complex networks.

Findings

Node-dependent resetting can optimize search efficiency.

Exact formulas for stationary occupation probabilities.

Validation through numerical simulations on different networks.

Abstract

In the present work, we study random walks on complex networks subject to stochastic resetting when the resetting probability is node-dependent. Using a renewal approach, we derive the exact expressions of the stationary occupation probabilities of the walker on each node and the mean first passage time between arbitrary two nodes. Finally, we demonstrate our theoretical results on three networks with two different resetting protocols, validated by numerical simulations as well. We find that under a delicate setting it is advantageous to optimize the efficiency of a global search on such networks by the node-dependent resetting probability.