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Stochastic Resetting Prevails Over Sharp Restart for Broad Target Distributions.

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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.

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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.