Robust random search with scale-free stochastic resetting

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Stochastic processes are fundamental to modeling various natural phenomena.
• Search strategies often face challenges with efficiency and parameter optimization.
• Resetting mechanisms in random walks can alter diffusion properties.

Purpose of the Study:

• Introduce a new search model based on stochastic resetting with time-dependent rates.
• Investigate the diffusion properties arising from this novel resetting protocol.
• Demonstrate the general applicability and efficiency of the proposed search-boosting method.

Main Methods:

• Developed a theoretical model for stochastic search with time-explicit resetting rates.
• Analyzed the mean-square displacement and propagator properties.
• Explored both subdiffusive and superdiffusive regimes using general rate functions.

Main Results:

• A resetting rate inversely proportional to time yields paradoxical diffusion.
• This paradoxical diffusion exhibits a mix of self-similarity, linear growth, nonlocality, and non-Gaussian behavior.
• The proposed protocol is robust and does not require optimization for specific search problem scales.

Conclusions:

• Time-dependent stochastic resetting offers a powerful and generalizable method for enhancing search efficiency.
• The model demonstrates unique diffusion characteristics, expanding the understanding of anomalous transport.
• This approach provides a parameter-insensitive strategy for optimizing search processes.