Format:
1 Online-Ressource (vii, 104 Seiten, 5865 KB)
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Illustrationen, Diagramme
Content:
This thesis focuses on the study of marked Gibbs point processes, in particular presenting some results on their existence and uniqueness, with ideas and techniques drawn from different areas of statistical mechanics: the entropy method from large deviations theory, cluster expansion and the Kirkwood--Salsburg equations, the Dobrushin contraction principle and disagreement percolation. We first present an existence result for infinite-volume marked Gibbs point processes. More precisely, we use the so-called entropy method (and large-deviation tools) to construct marked Gibbs point processes in R^d under quite general assumptions. In particular, the random marks belong to a general normed space S and are not bounded. Moreover, we allow for interaction functionals that may be unbounded and whose range is finite but random. The entropy method relies on showing that a family of finite-volume Gibbs point processes belongs to sequentially compact entropy level sets, and is therefore tight. We then present infinite-dimensional Langevin ...
Note:
Dissertation Universität Potsdam 2021
Additional Edition:
Erscheint auch als Druck-Ausgabe Zass, Alexander A multifaceted study of marked Gibbs point processes Potsdam, 2021
Language:
English
Keywords:
Hochschulschrift
DOI:
10.25932/publishup-51277
URN:
urn:nbn:de:kobv:517-opus4-512775
URL:
https://doi.org/10.25932/publishup-51277
URL:
https://nbn-resolving.org/urn:nbn:de:kobv:517-opus4-512775
URL:
https://d-nb.info/1238140548/34
Author information:
Poghosyan, Suren
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