Advances in Applied Probability

Mixing properties for STIT tessellations

R. Lachièze-Rey

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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.

Article information

Source
Adv. in Appl. Probab. Volume 43, Number 1 (2011), 40-48.

Dates
First available in Project Euclid: 15 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aap/1300198511

Digital Object Identifier
doi:10.1239/aap/1300198511

Mathematical Reviews number (MathSciNet)
MR2761143

Zentralblatt MATH identifier
1216.60012

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 05B45: Tessellation and tiling problems [See also 52C20, 52C22] 37A25: Ergodicity, mixing, rates of mixing

Keywords
Stochastic geometry random tessellation STIT tessellation space ergodicity mixing property

Citation

Lachièze-Rey, R. Mixing properties for STIT tessellations. Adv. in Appl. Probab. 43 (2011), no. 1, 40--48. doi:10.1239/aap/1300198511. https://projecteuclid.org/euclid.aap/1300198511.


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