期刊
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
卷 -, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2008/05/P05004
关键词
stochastic particle dynamics (theory); stationary states; zero-range processes; large deviations in non-equilibrium systems
资金
- EPSRC [EP/E030173/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/E030173/1] Funding Source: researchfish
We study the factorized 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(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 three distinct behaviours: at subcritical densities the distribution is Gumbel; at the critical density the distribution is Frechet, and above the critical density a different distribution emerges. We relate p(cond)(m) to the probability density of the largest mass in the system.
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