Random Walk on T-Fractal with Stochastic Resetting

Area of Science:

• Physics
• Complex Systems
• Network Science

Background:

• Random walks are fundamental models for transport and search processes.
• Fractal networks exhibit complex topological properties influencing diffusion dynamics.
• Stochastic resetting is a strategy to potentially enhance search efficiency.

Purpose of the Study:

• To investigate the effect of stochastic resetting on random walks on a T-fractal network.
• To determine the optimal resetting probability that minimizes mean first passage time.
• To compare search efficiency with and without resetting.

Main Methods:

• Utilized the generating function technique to analyze first passage time distributions.
• Derived a recursive relation for the generating function of first passage time.
• Calculated the mean first passage time (MFPT) with and without resetting.

Main Results:

• Established a relationship between MFPT with resetting and the generating function of FPT without resetting.
• Identified optimal resetting probabilities (γ*) for various scenarios.
• Demonstrated that stochastic resetting significantly improves search efficiency, particularly for larger networks.

Conclusions:

• Stochastic resetting is a powerful strategy for optimizing search processes in complex fractal networks.
• The findings offer insights into improving search efficiency in diverse applications.
• This study provides a theoretical framework for understanding resetting dynamics on fractal structures.