Szczegóły publikacji
Opis bibliograficzny
Universality of order statistics for Brownian reshuffling / Zdzisław BURDA, Mario Kieburg, Tomasz MACIOCHA // Physical Review . E ; ISSN 2470-0045. — Tytuł poprz.: Physical Review E, Statistical, nonlinear, and soft matter physics ; ISSN: 1539-3755. — 2026 — vol. 114 iss. 1 art. no. 014130, s. 014130-1-014130-12. — Bibliogr. s. 014130-12, Abstr. — Publikacja dostępna online od: 2026-07-16
Autorzy (3)
- AGHBurda Zdzisław
- Kieburg Mario
- AGHMaciocha Tomasz
Dane bibliometryczne
| ID BaDAP | 169347 |
|---|---|
| Data dodania do BaDAP | 2026-09-14 |
| Tekst źródłowy | URL |
| DOI | 10.1103/q2jj-5flv |
| Rok publikacji | 2026 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Physical Review, E |
Abstract
We discuss the order statistics of the particle positions of a gas of N identical independent particles performing Brownian motion in one dimension in a potential that asymptotically behaves like V (x) similar to x(gamma) for x -> +infinity, with a positive power gamma> 0. We show that in the stationary state, the order statistics that describe how the leaders are reshuffled are universal and independent of gamma . What depends on gamma is the timescale of the leaders' reshuffling, which scales as a power of the logarithm of the population size: t similar to (ln N) (2(1-gamma ))/(gamma) tau , where tau is of order one. We derive the probability that the particle which has the k-th largest value of x at some time t(1) will have the j-th largest value at time t(2) = t(1) + t in the form of an explicit expression for the generating function for the reshuffling probabilities for all k >= 1 and j >= 1. The generating function, expressed in scaled time tau , is independent of gamma . In particular, we show that the average percentage overlap coefficient of leader lists takes the universal, gamma -independent form erfc(root tau ) for long lists.
