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Mixing properties for STIT tessellations

Part of: Geometric probability and stochastic geometry Ergodic theory Designs and configurations

Published online by Cambridge University Press:  01 July 2016

R. Lachièze-Rey
R. Lachièze-Rey*
Affiliation:
Université des Sciences et Technologies de Lille
*
∗ Postal address: Laboratoire de Statistique et Probabilités, UFR de Mathematiques Bat. M2, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq, France. Email address: [email protected]
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Abstract

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The so-called STIT tessellations form a class of homogeneous (spatially stationary) tessellations in Rd which are stable under the nesting/iteration operation. In this paper we establish the mixing property for these tessellations and give the decay rate of P(A ∩ M = ∅, ThB ∩ M = ∅) / P(A ∩ Y = ∅)P(B ∩ Y = ∅) − 1, where A and B are both compact connected sets, h is a vector of Rd, Th is the corresponding translation operator, and M is a STIT tessellation.

Keywords

Stochastic geometryrandom tessellationSTIT tessellationspace ergodicitymixing property

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 05B45: Tessellation and tiling problems 37A25: Ergodicity, mixing, rates of mixing
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 43 , Issue 1 , March 2011 , pp. 40 - 48
Copyright
Copyright © Applied Probability Trust 2011 

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