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Regenerative processes for Poisson zero polytopes

  • Servet Martínez (a1) and Werner Nagel (a2)

Abstract

Let (Mt:t>0) be a Markov process of tessellations of ℝ, and let (𝒞t:t>0) be the process of their zero cells (zero polytopes), which has the same distribution as the corresponding process for Poisson hyperplane tessellations. In the present paper we describe the stationary zero cell process (at𝒞at:t∈ℝ),a>1, in terms of some regenerative structure and we show that it is a Bernoulli flow. An important application is to STIT tessellation processes.

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Corresponding author

* Postal address: Departamento Ingeniería Matemática and Centro Modelamiento Matemático, Universidad de Chile, UMI 2807 CNRS, Casilla 170-3, Correo 3, Santiago, Chile. Email address: smartine@dim.uchile.cl
** Postal address: Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, 07737 Jena, Germany. Email address: werner.nagel@uni-jena.de

References

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Keywords

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Regenerative processes for Poisson zero polytopes

  • Servet Martínez (a1) and Werner Nagel (a2)

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