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Stochastic Resetting Prevails Over Sharp Restart for Broad Target Distributions
1University of Edinburgh, SUPA, School of Physics and Astronomy, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom.
Physical Review Letters
|July 31, 2025
Summary
Stochastic resetting can speed up search processes. For targets at random distances, a specific "conjugate" target distribution optimizes resetting, outperforming fixed-interval resets for certain distributions.
Area of Science:
- Physics
- Statistical Mechanics
- Probability Theory
Background:
- Stochastic resetting reduces completion time in processes like diffusive search.
- Deterministic resetting (sharp restart) optimizes mean first passage time for fixed targets.
Purpose of the Study:
- Investigate resetting protocols for targets at random distances.
- Introduce and derive the "conjugate target distribution" for optimizing resetting.
- Compare stochastic resetting with sharp restart for various target distributions.
Main Methods:
- Mathematical derivation of the conjugate target distribution.
- Analysis of diffusion processes with resetting.
- Comparison of mean first passage times for different resetting strategies.
Main Results:
- Derived an explicit expression for the conjugate target distribution P_{T}^{*}(R) for diffusion in any dimension.
- Demonstrated that stochastic resetting is superior to sharp restart for target distributions with exponential or heavier tails.
Conclusions:
- The conjugate target distribution provides an optimal resetting strategy for randomly located targets.
- Stochastic resetting offers advantages over deterministic methods when target distributions are broad or heavy-tailed.
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