%0 Journal Article
%T The distribution of the zeroes of random trigonometric polynomials
%A Andrew Granville
%A Igor Wigman
%J Mathematics
%D 2008
%I arXiv
%X We study the asymptotic distribution of the number $Z_{N}$ of zeros of random trigonometric polynomials of degree $N$ as $N\to\infty$. It is known that as $N$ grows to infinity, the expected number of the zeros is asymptotic to $\frac{2}{\sqrt{3}}\cdot N$. The asymptotic form of the variance was predicted by Bogomolny, Bohigas and Leboeuf to be $cN$ for some $c>0$. We prove that $\frac{Z_{N}-\E Z_{N}}{\sqrt{cN}}$ converges to the standard Gaussian. In addition, we find that the analogous result is applicable for the number of zeros in short intervals.
%U http://arxiv.org/abs/0809.1848v2