Matern Cluster Process with Holes at the Cluster Centers
Abstract
Inspired by recent applications of point processes to biological nanonetworks, this paper presents a novel variant of a Mat\'ern cluster process (MCP) in which the points located within a certain distance from the cluster centers are removed. We term this new process the MCP with holes at the cluster center (MCP-H, in short). Focusing on the three-dimensional (3D) space, we first characterize the conditional distribution of the distance between an arbitrary point of a given cluster to the origin, conditioned on the location of that cluster, for both MCP and MCP-H. These distributions are shown to admit remarkably simple closed forms in the 3D space, which is not even possible in the simpler two-dimensional (2D) case. Using these distributions, the contact distance distribution and the probability generating functional (PGFL) are characterized for both MCP and MCP-H.
Cite
@article{arxiv.2210.06065,
title = {Matern Cluster Process with Holes at the Cluster Centers},
author = {Seyed Mohammad Azimi-Abarghouyi and Harpreet S. Dhillon},
journal= {arXiv preprint arXiv:2210.06065},
year = {2022}
}
Comments
Stochastic geometry, Mat\'ern cluster process, Poisson hole process, biological nanonetworks, wireless networks