Mixing properties for STIT tessellations. (English) Zbl 1216.60012

Summary: The so-called STIT tessellations form a class of homogeneous (spatially stationary) tessellations in \(\mathbb R^d\) 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 \(P(A \cap M = \emptyset , T_hB \cap M = \emptyset ) / P(A \cap Y = \emptyset )P(B \cap Y = \emptyset ) - 1\), where \(A\) and \(B\) are both compact connected sets, \(h\) is a vector of \(\mathbb R^d\), \(T_h\) is the corresponding translation operator, and \(M\) is a STIT tessellation.


60D05 Geometric probability and stochastic geometry
05B45 Combinatorial aspects of tessellation and tiling problems
37A25 Ergodicity, mixing, rates of mixing
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