Mixing Properties of Stationary Poisson Cylinder Models
- We study a particular class of stationary random closed sets in R^d called Poisson k-cylinder models (short: P-k-CM's) for k=1,...,d-1. We show that all P-k-CM's are weakly mixing and possess long-range correlations. Further, we derive necessary and sufficient conditions in terms of the directional distribution of the cylinders under which the corresponding P-k-CM is mixing. Regarding the P-(d-1)-CM as union of "thick hyperplanes" which generates a stationary process of polytopes we prove that the distribution of the polytope containing the origin does not depend on the thickness of the hyperplanes.
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| Author: | Christian Bräu, Lothar HeinrichGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-37694 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/3769 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2016-03) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2016/06/15 |
| Tag: | random closed set; hitting functional; random k-cylinder; independently marked Poisson process; tail sigma-algebra; typical cell; zero cell |
| GND-Keyword: | Zufällige Menge; Sigma-Algebra; Poisson-Prozess; Stochastische Geometrie |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht mit Print on Demand |
