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Stochastic resetting prevails over sharp restart for broad target distributions

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arxiv 2410.01941 v2 pith:JJHLC3WI submitted 2024-10-02 cond-mat.stat-mech

Martin R. Evans , Somrita Ray This is my paper · ORCID
classification cond-mat.stat-mech
keywords targettimeresettingdistributionconjugategivenrestartsharp
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abstract

Resetting has been shown to reduce the completion time for a stochastic process, such as the first passage time for a diffusive searcher to find a target. The time between two consecutive resetting events is drawn from a waiting time distribution $\psi(t)$, which defines the resetting protocol. Previously, it has been shown that deterministic resetting process with a constant time period, referred to as sharp restart, can minimize the mean first passage time to a fixed target. Here we consider the more realistic problem of a target positioned at a random distance $R$ from the resetting site, selected from a given target distribution $P_T(R)$. We introduce the notion of a conjugate target distribution to a given waiting time distribution. The conjugate target distribution, $P_T^*(R)$, is that $P_T(R)$ for which $\psi(t)$ extremizes the mean time to locate the target. In the case of diffusion we derive an explicit expression for $P^*_T(R)$ conjugate to a given $\psi(t)$ which holds in arbitrary spatial dimension. Our results show that stochastic resetting prevails over sharp restart for target distributions with exponential or heavier tails.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Strongly correlated stochastic systems

    cond-mat.stat-mech 2025-08 conditional novelty 6.0 of 10

    A unified formalism for conditionally independent variables produces exact large-N statistics for resetting gases and a switching-trap experiment.

  2. Thermodynamic Cost of Recurrent Erasure

    cond-mat.stat-mech 2025-02 conditional novelty 6.0 of 10

    For recurrent resetting via finite-time harmonic trap stiffness changes, the authors derive the mean and variance of the work and an optimal finite-time protocol whose quasistatic cost falls below the equilibrium free...

  3. A geometric approach to constructing quasi-isodynamic fields

    physics.plasm-ph 2025-08 unverdicted novelty 5.0 of 10

    The paper claims a direct geometric construction method for quasi-isodynamic stellarators, including elongation control and half-helicity axis families, but the provided full text is a different document, so the claim...

  4. Stochastic Resetting and Large Deviations

    cond-mat.stat-mech 2024-12 accept novelty 2.0 of 10

    A self-contained lecture-note introduction to diffusion with stochastic resetting, covering stationary states, first-passage properties, large deviations, and the cost of resetting.

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