The goal of this paper is to provide estimates leading to a direct proof of the exponential decay of the n-point correlation functions for certain unbounded models of Kac type. The methods are based on estimating higher order derivatives of the solution of the Witten Laplacian equation on one forms associated with the hamiltonian of the system. We also provide a formula for the Taylor coefficients of the pressure that is suitable for a direct proof the analyticity.
讨论了Laguerre级数$f (z) = \sum_{n=0}^{\infty} λ_{n}^{(α)} L_{n}^{(α)} (z)$到幂级数$f (z) = \sum_{n=0}^{\infty} γ_{n} z^{n}$的变换.许多非解析函数可以用这种方法展开。因此，不能保证成功。基于$λ_{n}^{(α)}$作为$n \to \infty$的衰减率和符号模式的简单充分条件可以被公式化，其保证$f (z$在$z=0$是解析的。如果$λ_{n}^{(α)}$以指数或因子形式衰减为$n \to \infty$，则得到有意义的结果。如果$λ_{n}^{(α)}$以代数方式衰变为$n \to \infty$，情况就复杂得多。如果$λ_{n}^{(α)}$最终具有相同的符号，则幂级数系数的级数展开式发散，并且相应的函数在$z=0. If the $ λ_{n}^{（α）} $ ultimately have strictly alternating signs, the series expansions for the power series coefficients are summable and the power series represents an analytic function. In the case of simple $ λ_{n}^{（α）} $, …
Uniqueness, analyticity and mixing for Gibbs point processes via spectral gaps
Hasso Plattner Institute, University of Potsdam（波茨坦大学哈索·普拉特纳研究所）；King’s College London, Department of Mathematics（伦敦国王学院数学系）；Northwestern University, Department of Mathematics（西北大学数学系）；Georgia Institute of Technology, School of Computer Science（佐治亚理工学院计算机学院）
