## Illinois Journal of Mathematics

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

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

#### Article information

Source
Illinois J. Math., Volume 45, Number 2 (2001), 559-580.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138356

Digital Object Identifier
doi:10.1215/ijm/1258138356

Mathematical Reviews number (MathSciNet)
MR1878619

Zentralblatt MATH identifier
1015.11034

Subjects
Primary: 60F15: Strong theorems

#### Citation

Berkes, István; Philipp, Walter; Tichy, Robert. Pair correlations and $U$-statistics for independent and weakly dependent random variables. Illinois J. Math. 45 (2001), no. 2, 559--580. doi:10.1215/ijm/1258138356. https://projecteuclid.org/euclid.ijm/1258138356