Approaches to asymptotics for U-statistics of Gibbs facet processes

TL;DR

This paper leverages the CLT for U-statistics of Poisson processes to derive asymptotic results for Gibbs facet processes, introducing a submodel for simplification and analyzing increasing intensity scenarios.

Contribution

It presents a novel approach to derive asymptotics for U-statistics of Gibbs facet processes using Poisson process CLT and a simplified submodel.

Findings

Asymptotic normality established for Gibbs facet process U-statistics

Simplified approach via a full-dimensional submodel

Asymptotics characterized for increasing intensity regimes

Abstract

It is shown how the central limit theorem for U-statistics of spatial Poisson point processes can help to derive the central limit theorem for U-statistics of a Gibbs facet process from stochastic geometry. A full-dimensional submodel enables a simpler approach to the investigation. Finally the general situation is studied and the asymptotics with increasing intensity is described.