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Random walks with stochastic resetting in complex networks: A discrete-time approach.
Thomas M Michelitsch1, Giuseppe D'Onofrio2, Federico Polito3
1Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, F-75005 Paris, France.
Chaos (Woodbury, N.Y.)
|January 9, 2025
Summary
This study analyzes random walks with resets on networks, finding that resets significantly improve searcher efficiency, especially in large-world networks like the Watts-Strogatz graph.
Area of Science:
- Complex systems
- Network science
- Stochastic processes
Background:
- Random walks are fundamental models for diffusion and search processes on networks.
- Reset mechanisms introduce non-Markovian dynamics, altering standard random walk behavior.
- Understanding first passage time statistics is crucial for optimizing search strategies.
Purpose of the Study:
- To investigate the impact of renewal process resets on first hitting time statistics in discrete-time random walks on networks.
- To analyze both Markovian and non-Markovian resetting protocols, including light- and fat-tailed inter-reset distributions.
- To explore the ergodicity and efficiency of resetting random walks on different network topologies.
Main Methods:
- Derivation of the propagator matrix using backward recurrence time probability density functions.
- Development of a defective propagator matrix to handle non-Markovian resetting and calculate mean first passage times.
- Analysis of inter-reset time distributions, including the Sibuya case with infinite mean.
- Application to Watts-Strogatz and Barabási-Albert random graphs to study resetting effects.
Main Results:
- Existence of a non-equilibrium steady state for light-tailed resetting processes.
- Sufficient conditions for ergodicity of resetting walks established, alongside a non-ergodic resetting mechanism.
- Demonstration of nontrivial dependencies of mean first passage time on network parameters and resetting rates.
- Significant enhancement of random searcher efficiency by resets in large-world Watts-Strogatz graphs.
Conclusions:
- Resetting mechanisms can fundamentally alter the dynamics and efficiency of random walks on networks.
- Non-Markovian resetting, particularly with fat-tailed distributions, presents unique challenges and behaviors.
- The study provides a framework for analyzing complex search dynamics and highlights the benefits of targeted resets in specific network structures.
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