The $\beta$-Mixing Rate of STIT Tessellations

TL;DR

This paper investigates the spatial dependence decay of homogeneous STIT tessellations in Euclidean space, demonstrating that their $eta$-mixing rate approaches zero, indicating increasing independence over distance.

Contribution

The paper establishes the convergence of the $eta$-mixing rate to zero for homogeneous STIT tessellations, providing new insights into their spatial dependence structure.

Findings

$eta$-mixing rate converges to zero for STIT tessellations

Shows increasing independence over larger spatial scales

Provides theoretical foundation for spatial statistical analysis

Abstract

We consider homogeneous STIT tessellations $Y$ in the $\ell$-dimensional Euclidean space $R^\ell$ and show that the (spatial) $\beta$-mixing rate converges to zero.