Ergodic description of STIT tessellations

Abstract

Let (Y-t : t > 0) be the STIT tessellation process. We show that for all polytopes W with nonempty interior and all a > 1, the renormalized random sequence (a(n)Y(an) : n is an element of Z) induced in W is a finitary factor of a Bernoulli shift. As a corollary, we get that the renormalized continuous time process (a(t)Y(at) : t is an element of R) induced in W is a Bernoulli flow.