经典气体的递归解析
Analyticity for classical gasses via recursion
摘要：
给出了具有排斥对势的经典气体的无限体积吉布斯测度唯一性和压力解析性的新判据。我们对解析性的界的改进是由一个因素$e^2$在经典的集群扩展方法和一个因素$e$在集群扩展收敛的已知限制。该标准是基于一个点过程的密度的递归计算的压缩属性。在我们的证明中的关键成分包括一个完整的身份的密度吉布斯点过程和适应的算法相关衰减方法从理论计算机科学。我们还从我们的结果推导出一个改进的边界的压力作为密度的函数的解析。
英文摘要：
We give a new criterion for a classical gas with a repulsive pair potential to exhibit uniqueness of the infinite volume Gibbs measure and analyticity of the pressure. Our improvement on the bound for analyticity is by a factor $e^2$ over the classical cluster expansion approach and a factor $e$ over the known limit of cluster expansion convergence. The criterion is based on a contractive property of a recursive computation of the density of a point process. The key ingredients in our proofs include an integral identity for the density of a Gibbs point process and an adaptation of the algorithmic correlation decay method from theoretical computer science. We also deduce from our results an improved bound for analyticity of the pressure as a function of the density.
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