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 $\{n_k\omega\}\mod 1$.
Citation
István Berkes. Walter Philipp. Robert Tichy. "Pair correlations and $U$-statistics for independent and weakly dependent random variables." Illinois J. Math. 45 (2) 559 - 580, Summer 2001. https://doi.org/10.1215/ijm/1258138356
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