Nearest Neighbour Distance Distribution in Hard-Core Point Processes

2016/06/12 by Al-Hourani, Akram, Evans, Robin J., Kandeepan, Sithamparanathan
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1606.03695

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 Matérn 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.

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