On the arrangement of cells in planar STIT and Poisson line tessellations

TL;DR

This paper investigates the differences in cell arrangements between planar STIT and Poisson line tessellations, focusing on neighboring cell characteristics and correlation functions of cell centers.

Contribution

It provides a comparative analysis of cell arrangements and correlation functions in STIT and Poisson line tessellations, highlighting structural differences.

Findings

Differences in neighboring cell arrangements are identified.

Pair-correlation and mark correlation functions are estimated and compared.

Structural distinctions between the tessellation models are characterized.

Abstract

It is well known that the distributions of the interiors of the typical cell of a Poisson line tessellation and a STIT tessellation with the same parameters coincide. In this paper, differences in the arrangement of the cells in these two tessellation models are investigated. In particular, characteristics of the set of cells neighbouring the typical cell are studied. Furthermore, the pair-correlation function and several mark correlation functions of the point processes of cell centres are estimated and compared.