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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.

Asymptotic Moments of Near Neighbor Distances for the Gaussian Distribution