| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2023-03-22T14:00:04Z |
| Last updated:
|
2023-08-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151587 |
| . |
| Reference:
|
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| . |
