## Advances in Applied Probability

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

### Mixing properties for STIT tessellations

#### Abstract

The so-called STIT tessellations form a class of homogeneous (spatially
stationary) tessellations in **R**^{d} 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* = ∅, *T*_{h}*B* ∩ *M* = ∅) /
P(*A* ∩ *Y* = ∅)P(*B* ∩ *Y* = ∅) - 1,
where *A* and *B* are both compact connected sets, *h* is a
vector of **R**^{d}, *T*_{h} 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