Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics
Journal of Applied Probability , Volume 57 - Issue 3 p. 928- 955
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 byproduct of our approach is a new uniqueness result for Gibbs particle processes.
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Beneš, V, Hofer-Temmel, C, Last, G, & Večeřa, J. (2020). Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics. Journal of Applied Probability, 57(3), 928–955. doi:10.1017/jpr.2020.51