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Distance statistics in random media

High dimension and/or high neighborhood order cases

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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 kth 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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Authors and Affiliations

  1. Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP), Universidade de São Paulo (USP), Avenida Bandeirantes, 3900, 14040-901, Ribeirão Preto, São Paulo, Brazil

    Cristiano Roberto Fabri Granzotti & Alexandre Souto Martinez

  2. National Institute of Science and Technology in Complex Systems (LNCT-SC), Universidade de São Paulo (USP), Avenida Bandeirantes, 3900, 14040-901, Ribeirão Preto, São Paulo, Brazil

    Alexandre Souto Martinez

Authors
  1. Cristiano Roberto Fabri Granzotti
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  2. Alexandre Souto Martinez
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Correspondence to Cristiano Roberto Fabri Granzotti.

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Granzotti, C., Souto Martinez, A. Distance statistics in random media. Eur. Phys. J. B 87, 87 (2014). https://doi.org/10.1140/epjb/e2014-50003-y

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  • DOI: https://doi.org/10.1140/epjb/e2014-50003-y

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