Pair correlations and $U$-statistics for independent and weakly dependent random variables
Berkes, István ; Philipp, Walter ; Tichy, Robert
Illinois J. Math., Tome 45 (2001) no. 4, p. 559-580 / Harvested from Project Euclid
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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 $\{n_k\omega\}\mod 1$.
Publié le : 2001-04-15
Classification:  60F15,  11K06 
@article{1258138356,
     author = {Berkes, Istv\'an and Philipp, Walter and Tichy, Robert},
     title = {Pair correlations and $U$-statistics for independent and weakly dependent random variables},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 559-580},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138356}
}

Berkes, István; Philipp, Walter; Tichy, Robert. Pair correlations and $U$-statistics for independent and weakly dependent random variables. Illinois J. Math., Tome 45 (2001) no. 4, pp.  559-580. http://gdmltest.u-ga.fr/item/1258138356/