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Stit Tessellations have Trivial Tail σ-Algebra

Part of: Ergodic theory Geometric probability and stochastic geometry Markov processes

Published online by Cambridge University Press:  22 February 2016

Servet Martínez  and
Werner Nagel
Servet Martínez*
Affiliation:
Universidad de Chile
Werner Nagel*
Affiliation:
Friedrich-Schiller-Universität Jena
*
∗ Postal address: Departamento Ingeniería Matemática and Centro Modelamiento Matemático, Universidad de Chile, UMI 2807 CNRS, Casilla 170-3, Correo 3, Santiago, Chile. Email address: smartine@dim.uchile.cl
∗∗ Postal address: Institut für Stochastik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany. Email address: werner.nagel@uni-jena.de
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Abstract

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We consider homogeneous STIT tessellations Y in the ℓ-dimensional Euclidean space ℝℓ and show the triviality of the tail σ-algebra. This is a sharpening of the mixing result by Lachièze-Rey (2001).

Keywords

Stochastic geometryrandom process of tessellationsergodic theorytail σ-algebra

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J75: Jump processes 37A25: Ergodicity, mixing, rates of mixing
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 46 , Issue 3 , September 2014 , pp. 643 - 660
Copyright
© Applied Probability Trust 

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