Strong mixing property for STIT tessellations

The so-called STIT tessellations form the class of homogeneous (spatially stationary) tessellations of ${\mathbb{R}}^d$ which are stable under the nesting/iteration operation. In this paper, we establish the strong mixing property for these tessellations and give the optimal form of the rate of decay for the quantity $|$\mathbb{P}$({A}\cap Y=\emptyset,T_h B \cap Y=\emptyset)-$\mathbb{P}$({A}\cap Y=\emptyset)$\mathbb{P}$({B}\cap Y=\emptyset)|$when$A$and$B$aretwocompactsets,$h$avectorof$$\mathbb{R}$^d$,$T_{h}$thecorrespondingtranslationoperatorand$Y$ a STIT Tessellation.