Theory of Probability and Mathematical Statistics
Pair correlations, beta distribution and hypergeometric functions
Christian Weiss
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Abstract: The N-point pair correlation statistic has been studied in detail for uniformly distributed sequences in the unit interval. Generically, the pair correlation statistic of uniformly distributed random sequences has so-called Poissonian pair correlation in its limit. For any (arbitrary) sequence in the unit interval, the N-point pair correlation static can by definition be bounded by N-1. In this paper, it is shown that any intermediate order of growth Nα with 0<α<1 can be realized by beta distributed random variables.
Keywords: Star-discrepancy, approximation of measures, discrete measures
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