Central limit theorem for Gibbsian U-statistics of facet processes

TL;DR

This paper establishes a central limit theorem for Gibbsian U-statistics of facet processes, providing asymptotic moment calculations and demonstrating normal convergence as the process intensity increases.

Contribution

It introduces a CLT for Gibbsian facet processes with discrete orientations, expanding understanding of their asymptotic behavior.

Findings

Asymptotic moments for interaction U-statistics are explicitly calculated.

A CLT is proven for the considered facet process as intensity grows.

The method of moments is used to derive the CLT.

Abstract

Special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic moments for interaction U-statistics are calculated and using the method of moments the central limit theorem is derived.