%0 Journal Article
%T Distance statistics in random media: high dimension and/or high neighborhood order cases
%A Cristiano Roberto Fabri Granzotti
%A Alexandre Souto Martinez
%J Physics
%D 2015
%I arXiv
%R 10.1140/epjb/e2014-50003-y
%X Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th nearest neighbor in a $d$-dimensional media. Next, we focus our attention in high dimensionality and high neighborhood order limits. High dimensionality makes distance distribution behavior as a delta sequence, with mean value equal to Cerf's conjecture. Distance statistics in high neighborhood order converges to a Gaussian distribution. The general distance statistics can be applied to detect departures from Poissonian point distribution hypotheses as proposed by Thompson and generalized here.
%U http://arxiv.org/abs/1508.02263v1