Diffusive transport on networks with stochastic resetting to multiple nodes

Abstract

We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first passage times. This general approach allows us to characterize the effect of resetting on the capacity of random walk strategies to reach a particular target or to explore the network. Our formalism holds for ergodic random walks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the efficiency of search strategies with resetting to multiple nodes. We apply the methods developed here to the dynamics with two reset nodes and derive analytical results for normal random walks and Lévy flights on rings. We also explore the effect of resetting to multiple nodes on a comb graph, Lévy flights that visit specific locations in a continuous space, and the Google random walk strategy on regular networks.

arXiv comment17 pages, 6 figures

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• Biased random walk on random networks in presence of stochastic resetting: Exact results
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• Optimal conditions for first passage of jump processes with resetting
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• A measure of dissimilarity between diffusive processes on networks
• Abrupt transitions in the optimization of diffusion with distributed resetting