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
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/3769
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2016-03)
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