Random walks on complex networks with multiple resetting nodes: A renewal approach

Area of Science:

• Statistical Physics
• Network Science
• Complex Systems

Background:

• Random walks are fundamental models for diffusion and transport processes.
• Stochastic resetting introduces periodic returns to specific locations, altering walk dynamics.
• Applications span diverse fields, including search algorithms and biophysics.

Purpose of the Study:

• To analyze discrete-time random walks on complex networks with multiple stochastic resetting nodes.
• To derive exact analytical expressions for walker occupation probabilities and mean first-passage times.
• To optimize resetting strategies for efficient global search on networks.

Main Methods:

• Utilized a renewal approach to derive exact analytical expressions.
• Leveraged spectral properties of the transition matrix in the absence of resetting.
• Employed a simulated annealing algorithm for optimizing resetting probability distributions.

Main Results:

• Derived exact expressions for occupation probability and mean first-passage time.
• Demonstrated the advantage of multiple resetting nodes for global search on various network types (circular, SBM, Barabási-Albert).
• Identified optimal resetting probability distributions that minimize average mean first-passage time.

Conclusions:

• Stochastic resetting, particularly with multiple resetting nodes, significantly enhances search efficiency on complex networks.
• The derived analytical framework provides a powerful tool for understanding and optimizing resetting processes.
• Optimized resetting strategies can substantially reduce traversal times in network exploration tasks.