Pair correlations and $U$ -statistics for independent and weakly dependent random variables

István Berkes, Walter Philipp, Robert Tichy

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Source: Crossref

Published: Apr 1, 2001

DOI: 10.1215/ijm/1258138356

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Source 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 $\{n_k\omega\}\mod 1$ .

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Pair correlations and $U$-statistics for independent and weakly dependent random variables — Mathematical Frontier Network