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March 2011 Mixing properties for STIT tessellations
R. Lachièze-Rey
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Adv. in Appl. Probab. 43(1): 40-48 (March 2011). DOI: 10.1239/aap/1300198511

Abstract

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(AM = ∅, ThBM = ∅) / P(AY = ∅)P(BY = ∅) - 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.

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R. Lachièze-Rey. "Mixing properties for STIT tessellations." Adv. in Appl. Probab. 43 (1) 40 - 48, March 2011. https://doi.org/10.1239/aap/1300198511

Information

Published: March 2011
First available in Project Euclid: 15 March 2011

zbMATH: 1216.60012
MathSciNet: MR2761143
Digital Object Identifier: 10.1239/aap/1300198511

Subjects:
Primary: 60D05
Secondary: 05B45 , 37A25

Keywords: mixing property , random tessellation , space ergodicity , STIT tessellation , Stochastic geometry

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 1 • March 2011
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