Ergodic Description of STIT Tessellations

2010/11/09 by Servet Martínez, Martínez, Servet, Werner Nagel +1
Mathematics · #37A25 #37A35 (Secondary) #60D05 (Primary) 60J25 #60J75 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:37A25 #msc:37A35 #msc:60D05 #msc:60J25 #msc:60J75

paper · pdf · doi:10.48550/arxiv.1011.1989

This is a preprint of an article submitted for consideration in the journal Stochastics: An International Journal of Probability and Stochastic Processes (copyright Taylor and Francis). Stochastics: An International Journal of Probability and Stochastic Processes is available online at http://www.informaworld.com/smpp/

arxiv created 2010/11/09 · arxiv updated 2010/11/10

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 (aⁿ Y_aⁿ: n integer) 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_a^t: t real) induced in W is a Bernoulli flow.

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