Exponential moments for planar tessellations
- Tóbiás, András
- Jahnel, Benedikt
2010 Mathematics Subject Classification
- 60K05 52A38 60G55
- 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
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 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.