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PAIR CORRELATIONS AND U-STATISTICS FOR INDEPENDENT AND WEAKLY DEPENDENT RANDOM VARIABLES

By István Berkes, Walter Philipp and Robert Tichy

Abstract

Abstract. We prove a Glivenko-Cantelli type strong law of large numbers for the pair correlation of independent random variables. Except for a few powers of logarithms the results obtained are sharp. Similar estimates hold for the pair correlation of lacunary sequences {nkω} mod 1. 1

Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.6436
Provided by: CiteSeerX
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