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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.01941 |
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| _version_ | 1866912439012950016 |
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| author | Evans, Martin R. Ray, Somrita |
| author_facet | Evans, Martin R. Ray, Somrita |
| contents | 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 $ψ(t)$, 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 $ψ(t)$ 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 $ψ(t)$ which holds in arbitrary spatial dimension. Our results show that stochastic resetting prevails over sharp restart for target distributions with exponential or heavier tails. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic resetting prevails over sharp restart for broad target distributions Evans, Martin R. Ray, Somrita Statistical Mechanics 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 $ψ(t)$, 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 $ψ(t)$ 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 $ψ(t)$ which holds in arbitrary spatial dimension. Our results show that stochastic resetting prevails over sharp restart for target distributions with exponential or heavier tails. |
| title | Stochastic resetting prevails over sharp restart for broad target distributions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2410.01941 |