STIT Tessellations have trivial tail \sigma-algebra

TL;DR

This paper proves that the tail algebra of homogeneous STIT tessellations in Euclidean space is trivial, refining previous mixing results and contributing to the understanding of their probabilistic structure.

Contribution

It establishes the triviality of the tail algebra for homogeneous STIT tessellations, sharpening earlier mixing results.

Findings

Proves the tail algebra is trivial for homogeneous STIT tessellations

Refines previous mixing results by Lachie8ze-Rey

Enhances understanding of the probabilistic structure of tessellations

Abstract

We consider homogeneous STIT tessellations Y in the \ell-dimensional Euclidean space and show the triviality of the tail \sigma-algebra. This is a sharpening of the mixing result by Lachi\`eze-Rey.