@article{EJP2403,
author = {Jean-Marc Azaïs and José León},
title = {CLT for crossings of random trigonometric polynomials},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {Crossings of random trigonometric polynomials; Rice formula; Chaos expansion},
abstract = {We establish a central limit theorem for the number of roots of the equation $X_N(t) =u$ when $X_N(t)$ is a Gaussian trigonometric polynomial of degree $N$. The case $u=0$ was studied by Granville and Wigman. We show that for some size of the considered interval, the asymptotic behavior is different depending on whether $u$ vanishes or not. Our mains tools are: a) a chaining argument with the stationary Gaussain process with covariance $\sin(t)/t$, b) the use of Wiener chaos decomposition that explains some singularities that appear in the limit when $u \neq 0$.},
pages = {no. 68, 1-17},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2403},
url = {http://ejp.ejpecp.org/article/view/2403}}