Exponential moments for planar tessellations

In this paper we show existence of all exponential moments for the total edge length in a unit disc for a family of planar tessellations based on Poisson point processes. Apart from classical such tessellations like the PoissonVoronoi, PoissonDelaunay and Poisson line tessellation, we also treat the JohnsonMehl tessellation, Manhattan grids, nested versions and Palm versions. As part of our proofs, for some planar tessellations, we also derive existence of exponential moments for the number of cells and the number of edges intersecting the unit disk.

Keywords

Poisson–Voronoi tessellation, Poisson–Delaunay tessellation, Poisson line tessellation, Johnson–Mehl tessellation, Manhattan grid, Cox–Voronoi tessellation, nested tessellation, iterated tessellation, exponential moments, total edge length, number of cells, number of edges, Palm calculus

URI

https://doi.org/10.34657/2341
https://oa.tib.eu/renate/handle/123456789/2755

Citation

Tóbiás, A., & Jahnel, B. (2019). Exponential moments for planar tessellations (Vol. 2572). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2572

Collections

Mathematik

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