Full Record Statistics of 1d Random Walks
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911925541011456 |
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| author | Régnier, Léo Dolgushev, Maxim Bénichou, Olivier |
| author_facet | Régnier, Léo Dolgushev, Maxim Bénichou, Olivier |
| contents | We develop a comprehensive framework for analyzing full record statistics, covering record counts $M(t_1), M(t_2), \ldots$, and their corresponding attainment times $T_{M(t_1)}, T_{M(t_2)}, \ldots$, as well as the intervals until the next record. From this multiple-time distribution, we derive general expressions for various observables related to record dynamics, including the conditional number of records given the number observed at a previous time and the conditional time required to reach the current record, given the occurrence time of the previous one. Our formalism is exemplified by a variety of stochastic processes, including biased nearest-neighbor random walks, asymmetric run-and-tumble dynamics, and random walks with stochastic resetting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_14885 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Full Record Statistics of 1d Random Walks Régnier, Léo Dolgushev, Maxim Bénichou, Olivier Statistical Mechanics Mathematical Physics Data Analysis, Statistics and Probability We develop a comprehensive framework for analyzing full record statistics, covering record counts $M(t_1), M(t_2), \ldots$, and their corresponding attainment times $T_{M(t_1)}, T_{M(t_2)}, \ldots$, as well as the intervals until the next record. From this multiple-time distribution, we derive general expressions for various observables related to record dynamics, including the conditional number of records given the number observed at a previous time and the conditional time required to reach the current record, given the occurrence time of the previous one. Our formalism is exemplified by a variety of stochastic processes, including biased nearest-neighbor random walks, asymmetric run-and-tumble dynamics, and random walks with stochastic resetting. |
| title | Full Record Statistics of 1d Random Walks |
| topic | Statistical Mechanics Mathematical Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2312.14885 |