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_hB ∩ 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.