Matérn cluster process with holes at the cluster centers

Seyed Mohammad Azimi-Abarghouyi and Harpreet S. Dhillon

Statistics & Probability Letters, 2024, vol. 204, issue C

Abstract: Inspired by recent applications of point processes to biological nanonetworks, this paper presents a novel variant of a Matérn 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.

Keywords: Stochastic geometry; Matérn cluster process; Poisson hole process; Biological nanonetworks; Wireless networks (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2023.109931

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