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Extremal statistics for a resetting Brownian motion before its first-passage time
Wusong Guo1, Hao Yan1, Hanshuang Chen1
1School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China.
Physical Review. E
|November 18, 2023
Summary
This study analyzes resetting Brownian motion, finding that increasing the resetting rate decreases maximum displacement. The time to reach maximum displacement shows a nonmonotonic dependence, with a minimum at an optimal rate.
Area of Science:
- Statistical physics
- Stochastic processes
Background:
- Brownian motion is a fundamental model for random processes.
- Resetting Brownian motion introduces periodic restarts, altering standard diffusion behavior.
Purpose of the Study:
- To investigate the extreme value statistics of one-dimensional resetting Brownian motion.
- To determine the distribution and expected value of maximum displacement and the time it is achieved.
Main Methods:
- Derivation of exit probability for resetting Brownian motion.
- Path decomposition technique in the Laplace domain.
- Extensive computer simulations for validation.
Main Results:
- Maximum displacement decreases monotonically with increasing resetting rate.
- Expected maximum displacement tends to 2x₀ as resetting rate approaches infinity.
- Expected time to maximum displacement exhibits nonmonotonic behavior, with a minimum at an optimal rate r*.
Conclusions:
- The resetting rate significantly influences both the magnitude and timing of maximum displacement in Brownian motion.
- An optimal resetting rate exists that minimizes the time to achieve maximum displacement.
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