Random walks on networks with stochastic resetting

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.