Condensation and Extreme Value Statistics
| dc.creator | Evans, Martin R. | |
| dc.creator | Majumdar, Satya N. | |
| dc.date | 2008-04-01 | |
| dc.date.accessioned | 2026-07-07T10:04:47Z | |
| dc.date.available | 2026-07-07T10:04:47Z | |
| dc.description | We study the factorised steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density the marginal distribution for the mass at a single site develops a bump, $p_{\rm cond}(m)$, at large mass $m$. This bump corresponds to a condensate site carrying a finite fraction of the mass in the system. Here, we study the condensation transition from a different aspect, that of extreme value statistics. We consider the cumulative distribution of the largest mass in the system and compute its asymptotic behaviour. We show 3 distinct behaviours: at subcritical densities the distribution is Gumbel; at the critical density the distribution is Fréchet, and above the critical density a different distribution emerges. We relate $p_{\rm cond}(m)$ to the probability density of the largest mass in the system. | |
| dc.description | 11 pages 2 figure | |
| dc.identifier | https://arxiv.org/abs/0804.0197 | |
| dc.identifier | http://arxiv.org/abs/0804.0197 | |
| dc.identifier | J. Stat. Mech. (2008) P05004 | |
| dc.identifier | doi:10.1088/1742-5468/2008/05/P05004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169806 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Condensation and Extreme Value Statistics | |
| dc.type | text |