3 research outputs found
Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics
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