The distribution of the zeros of random trigonometric polynomials
2011 (English)In: American Journal of Mathematics, Vol. 133, no 2, 295-357 p.Article in journal (Refereed) Published
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.
IdentifiersURN: urn:nbn:se:kth:diva-151232DOI: 10.1353/ajm.2011.0015ISI: 000288823800001ScopusID: 2-s2.0-80051623479OAI: oai:DiVA.org:kth-151232DiVA: diva2:747622
FunderKnut and Alice Wallenberg Foundation, KAW.2005.0098
QC 201409172014-09-172014-09-152014-09-17Bibliographically approved