Publikace na Matematicko-fyzikální fakulta |
2023
Abstrakt
This paper generalizes a recent existence result for infinite-volume marked Gibbs point processes. We try to use the existence theorem for two models from stochastic geometry.
First, we show the existence of Gibbs facet processes in Rd with repulsive interactions. We also prove that the finite-volume Gibbs facet processes with attractive interactions need not exist.
Afterwards, we study Gibbs-Laguerre tessellations of R2. The mentioned existence result cannot be used, since one of its assumptions is not satisfied for tessellations, but we are able to show the existence of an infinite-volume Gibbs-Laguerre process with a particular energy function, under the assumption that we almost surely see a point.