Biased random walks on networks with stochastic resetting

Area of Science:

• Complex Systems
• Network Science
• Statistical Physics

Background:

• Random walks are fundamental models for exploring networks.
• Stochastic resetting introduces a mechanism to confine random walkers.
• Biased random walks incorporate directionality into movement patterns.

Purpose of the Study:

• To investigate the impact of combining biased random walks with stochastic resetting on network exploration efficiency.
• To develop analytical tools for understanding search dynamics in complex networks.
• To assess the capacity of random walkers to reach targets and probe network structures.

Main Methods:

• Derivation of analytical expressions for stationary distribution and mean first passage time.
• Utilizing spectral representation of the probability transition matrix.
• Application of methods to pseudofractal scale-free webs and T-fractals.

Main Results:

• The combination of biased random walks and stochastic resetting significantly enhances search efficiency.
• Analytical expressions provide a method to quantify target reachability and network probing capacity.
• The study validates the approach on complex fractal network structures.

Conclusions:

• Biased random walks with stochastic resetting offer a powerful framework for efficient network exploration.
• The derived analytical expressions are generalizable to various complex network topologies.
• This work provides a strategy for analyzing larger and more intricate network structures.