摘要翻译：
我们证明了条件为超临界粒子密度的零程过程的不变测度的系综等价性的一个强形式。众所周知，在这种情况下，有一个单一的位点与系统中宏观上大量的粒子共存。我们证明了在热力学极限下，在临界密度下，其馀位点的联合分布等于巨正则测度。这改进了Gro\ss kinsky，Sch\"{u}tz和Spohn的结果，得到了有限维边缘的收敛性，作为推论，我们得到了分量的序统计量和体的涨落的极限定理。
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英文标题：
《Thermodynamic Limit for the Invariant Measures in Supercritical Zero
  Range Processes》
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作者：
In\'es Armend\'ariz, Michail Loulakis
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  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 Gro\ss kinsky, Sch\"{u}tz 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.
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PDF链接：
https://arxiv.org/pdf/801.2511