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The distribution of the zeros of random trigonometric polynomials
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Univ Montreal, Ctr Rech Math, Montreal, PQ H3C 3J7, Canada.
2011 (English)In: American Journal of Mathematics, ISSN 0002-9327, E-ISSN 1080-6377, Vol. 133, no 2, 295-357 p.Article in journal (Refereed) Published
Abstract [en]

We study the asymptotic distribution of the number Z N of zeros of random trigonometric polynomials of degree N as N →∞. It is known that as N grows to infinity, the expected number of the zeros is asymptotic to N. The asymptotic form of the variance was predicted by Bogomolny, Bohigas and Leboeuf to be cN for some c > 0. We prove that converges to the standard Gaussian. In addition, we find that the analogous result is applicable for the number of zeros in short intervals.

Place, publisher, year, edition, pages
2011. Vol. 133, no 2, 295-357 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-151232DOI: 10.1353/ajm.2011.0015ISI: 000288823800001Scopus ID: 2-s2.0-80051623479OAI: oai:DiVA.org:kth-151232DiVA: diva2:747622
Funder
Knut and Alice Wallenberg Foundation, KAW.2005.0098
Note

QC 20140917

Available from: 2014-09-17 Created: 2014-09-15 Last updated: 2017-12-05Bibliographically approved

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