Regenerative processes for Poisson zero polytopes

Abstract

Let $(M_t:t>0)$ be a Markov process of tessellations of ${\mathbb{R}}^{\ell }$ and $({\mathcal{C}}_t:t>0)$ the process of their zero cells (zero polytopes) which has the same distribution as the corresponding process for Poisson hyperplane tessellations. Let $a>1$. Here we describe the stationary zero cell process $(a^t{\mathcal{C}}_{a^t}:t\in \mathbb{R})$ in terms of some regenerative structure and we prove that it is a Bernoulli flow. An important application are the STIT tessellation processes.

Cited by in corpus (1)

• Tessellation-valued processes that are generated by cell division