Aging Record Statistics in Saturating Self-Interacting Random Walks
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914530426093568 |
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| author | Brémont, J. Voituriez, R. Bénichou, O. |
| author_facet | Brémont, J. Voituriez, R. Bénichou, O. |
| contents | The record age tau_k, defined as the time between the k-th and k+1-st record-breaking events, is a central observable of extreme-value statistics. In Markovian processes, the absence of memory makes tau_k independent of k. How memory breaks this invariance and induces aging, meaning a dependence of tau_k on k, remains a fundamental question, closely connected to widely observed aging phenomena in non-Markovian dynamics. In this Letter, we derive the exact asymptotic distribution of tau_k for saturating self-interacting random walks, a broad class of non-Markovian processes. We uncover two asymptotic regimes, in agreement with recent scaling predictions: at short times (tau much smaller than k squared), record statistics are governed by the geometry of the explored region, while at long times (tau much larger than k squared), memory effects become subdominant and reduce to nontrivial prefactor corrections. Our exact result provides a rare analytic window beyond scaling theory and extends to a framework that fully quantifies aging dynamics in the presence of saturating self-interaction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02433 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Aging Record Statistics in Saturating Self-Interacting Random Walks Brémont, J. Voituriez, R. Bénichou, O. Statistical Mechanics Probability The record age tau_k, defined as the time between the k-th and k+1-st record-breaking events, is a central observable of extreme-value statistics. In Markovian processes, the absence of memory makes tau_k independent of k. How memory breaks this invariance and induces aging, meaning a dependence of tau_k on k, remains a fundamental question, closely connected to widely observed aging phenomena in non-Markovian dynamics. In this Letter, we derive the exact asymptotic distribution of tau_k for saturating self-interacting random walks, a broad class of non-Markovian processes. We uncover two asymptotic regimes, in agreement with recent scaling predictions: at short times (tau much smaller than k squared), record statistics are governed by the geometry of the explored region, while at long times (tau much larger than k squared), memory effects become subdominant and reduce to nontrivial prefactor corrections. Our exact result provides a rare analytic window beyond scaling theory and extends to a framework that fully quantifies aging dynamics in the presence of saturating self-interaction. |
| title | Aging Record Statistics in Saturating Self-Interacting Random Walks |
| topic | Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2605.02433 |