Nearest Neighbour Distance Distribution in Hard-Core Point Processes

TL;DR

This paper develops an analytical framework to determine the distribution of nearest neighbor distances in hard-core point processes, specifically applying it to the Matérn hard-core process and validating results with simulations.

Contribution

Introduces a new analytical approach for the distribution of nearest neighbor distances in hard-core point processes, with explicit formulas for the Matérn process and multiple interaction cases.

Findings

Derived the cumulative distribution function for contact distances in MHC.

Validated analytical results with Monte-Carlo simulations.

Provided insights into spatial interactions in hard-core processes.

Abstract

In this paper we present an analytic framework for formulating the statistical distribution of the nearest neighbour distance in hard-core point processes. We apply this framework to Mat\'{e}rn hard-core point process (MHC) to derive the cumulative distribution function of the contact distance in three cases. The first case is between a point in an MHC process and its nearest neighbour from the same process. The second case is between a point in an independent Poisson point process and the nearest neighbour from an MHC process. The third case is between a point in the complement of an MHC process and its sibling MHC process. We test the analytic results against Monte-Carlo simulations to verify their consistency.