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CLT for crossings of random trigonometric polynomials


 
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1. Title Title of document CLT for crossings of random trigonometric polynomials
 
2. Creator Author's name, affiliation, country Jean-Marc Azaïs; Université de Toulouse; France
 
2. Creator Author's name, affiliation, country José R León; Universidad Central de Venezuela; Venezuela
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Crossings of random trigonometric polynomials; Rice formula; Chaos expansion
 
3. Subject Subject classification 60G15
 
4. Description 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 $u \neq 0$.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2013-07-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2403
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2403
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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