Kai-Uwe Schmidt
Published 2014-04-01, updated 2015-02-03Version 2
Three measures of pseudorandomness of finite binary sequences were introduced by Mauduit and S\'ark\"ozy in 1997 and have been studied extensively since then: the normality measure, the well-distribution measure, and the correlation measure of order r. Our main result is that the correlation measure of order r for random binary sequences converges strongly, and so has a limiting distribution. This solves a problem due to Alon, Kohayakawa, Mauduit, Moreira, and R\"odl. We also show that the best known lower bounds for the minimum values of the correlation measures are simple consequences of a celebrated result due to Welch, concerning the maximum nontrivial scalar products over a set of vectors.
Comments: 19 pages, this version contains small changes taking into account referee comments
On the Distribution Function of the Complexity of Finite Sequences
On the correlation measure of a family of commuting Hermitian operators with applications to particle densities of the quasi-free representations of the CAR and CCR
Spiked Models in Wishart Ensemble
![QR code for arXiv:1404.0172 [math.PR]](http://oss.arxitics.com/images/favicon.svg)