English

Exponential moments for planar tessellations

Probability 2020-11-24 v3

Abstract

In this paper we show existence of all exponential moments for the total edge length in a unit disk for a family of planar tessellations based on stationary point processes. Apart from classical such tessellations like the Poisson-Voronoi, Poisson-Delaunay and Poisson line tessellation, we also treat the Johnson-Mehl 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.

Cite

@article{arxiv.1902.02148,
  title  = {Exponential moments for planar tessellations},
  author = {András Tóbiás and Benedikt Jahnel},
  journal= {arXiv preprint arXiv:1902.02148},
  year   = {2020}
}

Comments

19 pages, 1 figure

R2 v1 2026-06-23T07:33:31.566Z