English

Nearest Neighbour Distance Distribution in Hard-Core Point Processes

Information Theory 2016-06-14 v1 math.IT

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.

Cite

@article{arxiv.1606.03695,
  title  = {Nearest Neighbour Distance Distribution in Hard-Core Point Processes},
  author = {Akram Al-Hourani and Robin J. Evans and Sithamparanathan Kandeepan},
  journal= {arXiv preprint arXiv:1606.03695},
  year   = {2016}
}
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