Beyond the Arcsine Law: Exact Two-Time Statistics of the Occupation Time in Jump Processes
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918178384248832 |
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| author | Plaud, Arthur Bénichou, Olivier |
| author_facet | Plaud, Arthur Bénichou, Olivier |
| contents | Occupation times quantify how long a stochastic process remains in a region, and their single-time statistics are famously given by the arcsine law for Brownian and Lévy processes. By contrast, two-time occupation statistics, which directly probe temporal correlations and aging, have resisted exact characterization beyond renewal processes. In this Letter we derive exact results for generic one-dimensional jump processes, a central framework for intermittent and discretely sampled dynamics. Using generalized Wiener-Hopf methods, we obtain the joint distribution of occupation time and position, the aged occupation-time law, and the autocorrelation function. In the continuous-time scaling limit, universal features emerge that depend only on the tail of the jump distribution, providing a starting point for exploring aging transport in complex environments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beyond the Arcsine Law: Exact Two-Time Statistics of the Occupation Time in Jump Processes Plaud, Arthur Bénichou, Olivier Statistical Mechanics Probability Occupation times quantify how long a stochastic process remains in a region, and their single-time statistics are famously given by the arcsine law for Brownian and Lévy processes. By contrast, two-time occupation statistics, which directly probe temporal correlations and aging, have resisted exact characterization beyond renewal processes. In this Letter we derive exact results for generic one-dimensional jump processes, a central framework for intermittent and discretely sampled dynamics. Using generalized Wiener-Hopf methods, we obtain the joint distribution of occupation time and position, the aged occupation-time law, and the autocorrelation function. In the continuous-time scaling limit, universal features emerge that depend only on the tail of the jump distribution, providing a starting point for exploring aging transport in complex environments. |
| title | Beyond the Arcsine Law: Exact Two-Time Statistics of the Occupation Time in Jump Processes |
| topic | Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2510.25859 |