Nearest Neighbor Distance Distribution in Hard-Core Point Processes

Abstract

In this letter, we present an analytic framework for formulating the statistical distribution of the nearest neighbor 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 neighbor from the same process. The second case is between a point in an independent Poisson point process and the nearest neighbor 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.