STIT Tessellations -- Ergodic Limit Theorems and Bounds for the Speed of Convergence

We consider homogeneous STIT tessellations in the $\ell$-dimensional Euclidean space ${\mathbb R}^\ell$. Based on results for the spatial $\beta$-mixing coefficient an upper bound for the variance of additive functionals of tessellations is derived, using results by Yoshihara and Heinrich. Moreover, ergodic theorems are applied to subadditive functionals.