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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/7868
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dc.contributor.authorMajumdar, Satya N-
dc.contributor.authorMouniax, Philippe-
dc.contributor.authorSabhapandit, Sanjib-
dc.contributor.authorSchehr, Gregory-
dc.date.accessioned2022-01-07T06:37:19Z-
dc.date.available2022-01-07T06:37:19Z-
dc.date.issued2022-01-
dc.identifier.citationJournal of Physics A : Mathematical and Theoretical, 2022, Vol. 55, p034002en_US
dc.identifier.issn1751-8113-
dc.identifier.issn1751-8121 (Online)-
dc.identifier.urihttp://hdl.handle.net/2289/7868-
dc.descriptionRestricted Access. An open-access version is available at arXiv.org (one of the alternative locations)en_US
dc.description.abstractWe compute exactly the mean number of records ⟨RN⟩ for a time-series of size N whose entries represent the positions of a discrete time random walker on the line with resetting. At each time step, the walker jumps by a length η drawn independently from a symmetric and continuous distribution f(η) with probability 1 − r (with 0 ⩽ r < 1) and with the complementary probability r it resets to its starting point x = 0. This is an exactly solvable example of a weakly correlated time-series that interpolates between a strongly correlated random walk series (for r = 0) and an uncorrelated time-series (for (1 − r) ≪ 1). Remarkably, we found that for every fixed $r\in \left[\right.0,1\left[\right.$ and any N, the mean number of records ⟨RN⟩ is completely universal, i.e. independent of the jump distribution f(η). In particular, for large N, we show that ⟨RN⟩ grows very slowly with increasing N as $\langle {R}_{N}\rangle \approx (1/\sqrt{r})\mathrm{ln}\enspace N$ for 0 < r < 1. We also computed the exact universal crossover scaling functions for ⟨RN⟩ in the two limits r → 0 and r → 1. Our analytical predictions are in excellent agreement with numerical simulations.en_US
dc.language.isoenen_US
dc.publisherIOP Publishing Ltd.en_US
dc.relation.urihttps://arxiv.org/abs/2110.01539en_US
dc.relation.urihttps://doi.org/10.1088/1751-8121/ac3fc1en_US
dc.relation.urihttps://ui.adsabs.harvard.edu/abs/2021arXiv211001539M/abstracten_US
dc.rights2022 IOP Publishing Ltd.en_US
dc.subjectrecord statisticsen_US
dc.subjectresetting dynamicsen_US
dc.subjectrandom walksen_US
dc.subjectextreme statisticsen_US
dc.titleRecord statistics for random walks and levy flights with resettingen_US
dc.typeArticleen_US
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