Advances in Applied Probability

Mixing properties for STIT tessellations

R. Lachièze-Rey

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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(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

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

First available in Project Euclid: 15 March 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Stochastic geometry random tessellation STIT tessellation space ergodicity mixing property


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

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