Optimizing Leapover Lengths of Lévy Flights with Resetting
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929464835833856 |
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| author | Radice, Mattia Cristadoro, Giampaolo |
| author_facet | Radice, Mattia Cristadoro, Giampaolo |
| contents | We consider a one-dimensional search process under stochastic resetting conditions. A target is located at $b\geq0$ and a searcher, starting from the origin, performs a discrete-time random walk with independent jumps drawn from a heavy-tailed distribution. Before each jump, there is a given probability $r$ of restarting the walk from the initial position. The efficiency of a "myopic search" - in which the search stops upon crossing the target for the first time - is usually characterized in terms of the first-passage time $τ$. On the other hand, great relevance is encapsulated by the leapover length $l = x_τ - b$, which measures how far from the target the search ends. For symmetric heavy-tailed jump distributions, in the absence of resetting the average leapover is always infinite. Here we show instead that resetting induces a finite average leapover $\ell_b(r)$ if the mean jump length is finite. We compute exactly $\ell_b(r)$ and determine the condition under which resetting allows for nontrivial optimization, i.e., for the existence of $r^*$ such that $\ell_b(r^*)$ is minimal and smaller than the average leapover of the single jump. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimizing Leapover Lengths of Lévy Flights with Resetting Radice, Mattia Cristadoro, Giampaolo Statistical Mechanics We consider a one-dimensional search process under stochastic resetting conditions. A target is located at $b\geq0$ and a searcher, starting from the origin, performs a discrete-time random walk with independent jumps drawn from a heavy-tailed distribution. Before each jump, there is a given probability $r$ of restarting the walk from the initial position. The efficiency of a "myopic search" - in which the search stops upon crossing the target for the first time - is usually characterized in terms of the first-passage time $τ$. On the other hand, great relevance is encapsulated by the leapover length $l = x_τ - b$, which measures how far from the target the search ends. For symmetric heavy-tailed jump distributions, in the absence of resetting the average leapover is always infinite. Here we show instead that resetting induces a finite average leapover $\ell_b(r)$ if the mean jump length is finite. We compute exactly $\ell_b(r)$ and determine the condition under which resetting allows for nontrivial optimization, i.e., for the existence of $r^*$ such that $\ell_b(r^*)$ is minimal and smaller than the average leapover of the single jump. |
| title | Optimizing Leapover Lengths of Lévy Flights with Resetting |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2403.12727 |