---
author:
- 'Jakub Večeřa, Viktor Beneš'
title: |
    Interaction processes for unions of facets,\
    a limit behavior
---

Charles University in Prague, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Sokolovská 83, 18675 Praha 8-Karlín, Czech Republic, vecera@karlin.mff.cuni.cz, benesv@karlin.mff.cuni.cz

[**Abstract**]{}

In the series of models with interacting particles in stochastic geometry, a further contribution presents the facet process which is defined in arbitrary Euclidean dimension. In 2D, 3D specially it is a process of interacting segments, flat surfaces, respectively. Its investigation is based on the theory of functionals of finite spatial point processes given by a density with respect to a Poisson process. The methodology based on $L_2$ expansion of the covariance of functionals of Poisson process is developed for $U$-statistics of facet intersections which are building blocks of the model. The importance of the concept of correlation functions of arbitrary order is emphasized. Some basic properties of facet processes, such as local stability and repulsivness are shown and a standard simulation algorithm mentioned. Further the situation when the intensity of the process tends to infinity is studied. In the case of Poisson processes a central limit theorem follows from recent results of Wiener-Ito theory. In 