Extreme Values of Infinite-Measure Processes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910043344994304 |
|---|---|
| author | Baravi, Talia Barkai, Eli |
| author_facet | Baravi, Talia Barkai, Eli |
| contents | We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in the long-time limit, by a non-normalizable infinite invariant density. Extreme events in such systems emerge in a joint limit where the observation time $t$ is long and the number of variables $N$ is large. We show that the resulting extreme value statistics are controlled by the return exponent $α$ and the infinite invariant measure, and therefore depart from the classical Fréchet, Gumbel, and Weibull universality classes. We illustrate the theory for weakly chaotic intermittent maps, overdamped diffusion in an asymptotically flat potential, and a stochastic model of sub-recoil laser cooling, and show how measurements of extremes can be used to infer the infinite-density structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05390 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extreme Values of Infinite-Measure Processes Baravi, Talia Barkai, Eli Statistical Mechanics We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in the long-time limit, by a non-normalizable infinite invariant density. Extreme events in such systems emerge in a joint limit where the observation time $t$ is long and the number of variables $N$ is large. We show that the resulting extreme value statistics are controlled by the return exponent $α$ and the infinite invariant measure, and therefore depart from the classical Fréchet, Gumbel, and Weibull universality classes. We illustrate the theory for weakly chaotic intermittent maps, overdamped diffusion in an asymptotically flat potential, and a stochastic model of sub-recoil laser cooling, and show how measurements of extremes can be used to infer the infinite-density structure. |
| title | Extreme Values of Infinite-Measure Processes |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2603.05390 |