Thermodynamic limit for the invariant measures in supercritical zero range processes

• 成果类型: Article
• 署名作者: Armendariz, Ines; Loulakis, Michail
• 署名单位: Universidad de San Andres Argentina; Universidade de Sao Paulo; University of Crete
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0165-7
• 发表日期: 2009
• 页码: 175-188
• 关键词: condensation

摘要

We prove a strong form of the equivalence of ensembles for the invariant measures of zero range processes conditioned to a supercritical density of particles. It is known that in this case there is a single site that accomodates a macroscopically large number of the particles in the system. We show that in the thermodynamic limit the rest of the sites have joint distribution equal to the grand canonical measure at the critical density. This improves the result of Grosskinsky, Schutz and Spohn, where convergence is obtained for the finite dimensional marginals. We obtain as corollaries limit theorems for the order statistics of the components and for the fluctuations of the bulk.