Decorrelation of a class of Gibbs particle processes and asymptotic properties of U -statistics

Viktor Beneš, Christoph Hofer-Temmel, Günter Last, Jakub Večeřa

Published 2019-03-15Version 1

We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of a non-negative pair potential and an activity parameter. For small activity parameters, we prove a central limit theorem for certain $U$-statistics of this Gibbs particle process. To this end we establish an exponential decorrelation property, a result of independent interest.