We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation, we prove exponential decay of the correlation functions, provided a dominating Boolean model is subcritical. We also prove this property for the weighted moments of a U-statistic of the process. Under the assumption of a suitable lower bound on the variance, this implies a central limit theorem for such U-statistics of the Gibbs particle process. A by-product of our approach is a new uniqueness result for Gibbs particle processes.

中文翻译：

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一类吉布斯粒子过程的去相关与U统计量的渐近性质

我们研究了一个静止的吉布斯粒子过程，在欧几里得空间上具有确定性有界粒子，根据活动参数和有限范围的非负相互作用势定义。使用分歧渗透，我们证明了相关函数的指数衰减，前提是主导布尔模型是次临界的。我们还为 a 的加权矩证明了这个性质ü-过程统计。在方差合适的下限的假设下，这意味着这样的中心极限定理ü-吉布斯粒子过程的统计量。我们方法的一个副产品是吉布斯粒子过程的一个新的唯一性结果。