Strong mixing property for STIT tessellations

2009/05/08 by Raphaël Lachièze-Rey, Lachièze-Rey, Raphaël
Mathematics · #60D05 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #math.DS #math.PR #msc:60D05

paper · pdf · doi:10.48550/arxiv.0905.1145

16 pages

arxiv created 2009/05/17 · arxiv updated 2009/12/01

Abstract

The so-called STIT tessellations form the class of homogeneous (spatially stationary) tessellations of 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 |ℙ(A∩ Y=∅,T_h B ∩ Y=∅)-ℙ(A∩ Y=∅)ℙ(B∩ Y=∅)| when A and B are two compact sets, h a vector of ℝ^d, T_h the corresponding translation operator and Y a STIT Tessellation.

Related

• The β-Mixing Rate of STIT Tessellations
• STIT Tessellations -- Ergodic Limit Theorems and Bounds for the Speed of\n Convergence
• Typical Geometry, Second-Order Properties and Central Limit Theory for Iteration Stable Tessellations
• STIT Tessellations have trivial tail σ-algebra
• A Proof of a Conjecture by Mecke for STIT tessellations