| Título: | CLT for crossings of random trigonometric polynomials |
| Autores: |
Azaïs, Jean-Marc; Université de Toulouse León, José R; Universidad Central de Venezuela |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Crossings of random trigonometric polynomials; Rice formula; Chaos expansion 60G15 |
| Descripción: | 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 $u \neq 0$. |
| Idioma: | Inglés |
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