# Exponential moments for planar tessellations

## TL;DR

This paper proves the existence of all exponential moments for the total edge length in various planar tessellations based on stationary point processes, including classical and more complex types.

## Contribution

It establishes exponential moment existence for total edge length and other features across a broad class of planar tessellations, extending prior results.

## Key findings

- Existence of exponential moments for total edge length in multiple tessellations
- Exponential moments for the number of cells and edges in some tessellations
- Application to classical and novel tessellation models

## 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.