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Related Experiment Video

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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Random walks on networks with stochastic resetting.

Alejandro P Riascos¹, Denis Boyer¹, Paul Herringer²

¹Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, México.

Physical Review. E

|July 22, 2020

Summary

We analyzed random walks with stochastic resetting on networks. Resetting enhances a walker's ability to find targets and explore networks efficiently, applicable to various network structures.

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Area of Science:

Network science
Statistical physics
Complex systems

Background:

Random walks are fundamental models for exploring networks.
Stochastic resetting introduces a mechanism to return to the origin, altering exploration dynamics.
Understanding resetting effects on network exploration is crucial for search strategies.

Purpose of the Study:

To investigate the impact of stochastic resetting on random walks across arbitrary networks.
To quantify how resetting affects target acquisition and network exploration efficiency.
To develop a general formalism for analyzing resetting processes on diverse network topologies.

Main Methods:

Derivation of stationary probability distributions for resetting random walks.
Calculation of mean and global first passage times.
Application of spectral properties of the underlying random walk (without resetting).

Main Results:

Obtained analytical results for stationary distributions and passage times.
Characterized the influence of resetting on search efficiency and exploration capacity.
Demonstrated applicability to various networks including rings, trees, and complex networks.

Conclusions:

Stochastic resetting can significantly enhance the efficiency of random walkers on networks.
The developed formalism provides a tool to analyze search strategies in networks with small-world or community structures.
This work extends the study of resetting phenomena to the broad domain of network science.