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

## TL;DR

This paper investigates the correlation decay and asymptotic behavior of U-statistics in Gibbs particle processes, establishing exponential decay, a central limit theorem, and a new uniqueness result under certain conditions.

## Contribution

It introduces a novel approach using disagreement percolation to prove correlation decay and CLT for Gibbs particle processes with bounded particles.

## Key findings

- Exponential decay of correlation functions under subcritical conditions.
- Central limit theorem for U-statistics of the process.
- A new uniqueness result for Gibbs particle processes.

## Abstract

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.