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Title: A note on the existence of Gibbs marked point processes with applications in stochastic geometry (English)
Author: Petráková, Martina
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 59
Issue: 1
Year: 2023
Pages: 130-159
Summary lang: English
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Category: math
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Summary: 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 $\mathbb{R}^d$ 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 $\mathbb{R}^2$. 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. (English)
Keyword: infinite-volume Gibbs measure
Keyword: existence
Keyword: Gibbs facet process
Keyword: Gibbs–Laguerre tessellation
MSC: 60D05
MSC: 60G55
idZBL: Zbl 07675646
idMR: MR4567845
DOI: 10.14736/kyb-2023-1-0130
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Date available: 2023-03-22T14:00:04Z
Last updated: 2023-08-04
Stable URL: http://hdl.handle.net/10338.dmlcz/151587
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