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Matérn cluster process with holes at the cluster centers

Author

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  • Azimi-Abarghouyi, Seyed Mohammad
  • Dhillon, Harpreet S.

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.

Suggested Citation

  • Azimi-Abarghouyi, Seyed Mohammad & Dhillon, Harpreet S., 2024. "Matérn cluster process with holes at the cluster centers," Statistics & Probability Letters, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:stapro:v:204:y:2024:i:c:s0167715223001554
    DOI: 10.1016/j.spl.2023.109931
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