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arXiv · 1508.02263

Distance statistics in random media: high dimension and/or high neighborhood order cases

Cristiano Roberto Fabri Granzotti·Alexandre Souto Martinez
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Abstract

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.

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Cristiano Roberto Fabri Granzotti, Alexandre Souto Martinez. 2015-08-10. Distance statistics in random media: high dimension and/or high neighborhood order cases. https://doi.org/10.1140/epjb%2Fe2014-50003-y

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