The Moment Generating function for ray lengths in the Half Gilbert Model with Rectangular Cells

TL;DR

This paper derives an exact expression for the moment generating function of ray lengths in a half rectangular Gilbert tessellation model, where certain directions of rays do not interact, advancing understanding of spatial stochastic processes.

Contribution

It introduces a novel exact formula for the moment generating function in the half rectangular Gilbert model, extending previous work to a new non-interacting ray configuration.

Findings

Derived an exact expression for the moment generating function.

Provides insights into the distribution of ray lengths in the model.

Extends mathematical understanding of spatial Poisson processes.

Abstract

In the full rectangular version of Gilbert's tessellation lines extend either horizontally (with east- and west--growing rays) or vertically (north- and south--growing rays) from seed points which form a Poisson point process, each ray stopping when another ray is met. In the half rectangular version, east and south growing rays do not interact with west and north rays. Using techniques developed in our previous paper, we derive an exact expression for the moment generating function for the ray length distribution in the half rectangular model.