From Maximum of Intervisit Times to Starving Random Walks
| Autor: | Régnier, L., Dolgushev, M., Bénichou, O. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Phys. Rev. Lett. 132, 127101 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.132.127101 |
| Popis: | Very recently, a fundamental observable has been introduced and analyzed to quantify the exploration of random walks: the time $\tau_k$ required for a random walk to find a site that it never visited previously, when the walk has already visited $k$ distinct sites. Here, we tackle the natural issue of the statistics of $M_n$, the longest duration out of $\tau_0,\dots,\tau_{n-1}$. This problem belongs to the active field of extreme value statistics, with the difficulty that the random variables $\tau_k$ are both correlated and non-identically distributed. Beyond this fundamental aspect, we show that the asymptotic determination of the statistics of $M_n$ finds explicit applications in foraging theory and allows us to solve the open $d$-dimensional starving random walk problem, in which each site of a lattice initially contains one food unit, consumed upon visit by the random walker, which can travel $\mathcal{S}$ steps without food before starving. Processes of diverse nature, including regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, share common properties within the same universality classes. Comment: 6 pages, 3 figures + 16 pages, 11 figures |
| Databáze: | arXiv |
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