First-passage times under frequent stochastic resetting

Area of Science:

• Statistical Physics
• Stochastic Processes
• Search Theory

Background:

• Stochastic search processes are fundamental in many scientific fields.
• Understanding first passage time is crucial for analyzing search efficiency.
• Stochastic resetting is a technique to enhance search processes.

Purpose of the Study:

• To determine the full distribution and moments of first passage time for stochastic search processes under frequent resetting.
• To develop a general framework applicable to various resetting time distributions.
• To analyze the accuracy of approximations in the limit of frequent resetting.

Main Methods:

• Analysis of stochastic processes in the limit of frequent resetting.
• Derivation of first passage time distributions and moments.
• Mathematical proofs for a wide class of search processes.
• Numerical illustrations and error analysis for diffusive search scenarios.

Main Results:

• The full distribution and moments of first passage time are determined for a broad class of stochastic search processes with frequent resetting.
• The derived results are valid for any system where the short-time behavior without resetting is known.
• Exponentially fast vanishing errors are demonstrated for approximations in typical diffusive search scenarios.
• The framework accommodates various resetting time distributions beyond the typical exponential case.

Conclusions:

• Frequent stochastic resetting significantly impacts the first passage time properties of search processes.
• The developed analytical framework provides accurate predictions for search efficiency under resetting.
• The findings offer valuable insights for optimizing search strategies in diverse scientific and technological applications.