Electronic Journal of Probability

Asymptotic Moments of Near Neighbor Distances for the Gaussian Distribution

Elia Liitiäinen

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We study the moments of the k-th nearest neighbor distance for independent identically distributed points in $\mathbb{R}^n$. In the earlier literature, the case with power higher than n has been analyzed by assuming a bounded support for the underlying density. The boundedness assumption is removed by assuming the multivariate Gaussian distribution. In this case, the nearest neighbor distances show very different behavior in comparison to earlier results.

Article information

Electron. J. Probab., Volume 16 (2011), paper no. 92, 2545-2573.

Accepted: 3 December 2011
First available in Project Euclid: 1 June 2016

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Zentralblatt MATH identifier

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

nearest neighbor moments gaussian random geometry

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Liitiäinen, Elia. Asymptotic Moments of Near Neighbor Distances for the Gaussian Distribution. Electron. J. Probab. 16 (2011), paper no. 92, 2545--2573. doi:10.1214/EJP.v16-969. https://projecteuclid.org/euclid.ejp/1464820261

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