Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/64171

Asymptotics of the variance of the number of real roots of random trigonometric polynomials

Authors Su, Zhonggen
Shao, Qiman View this author's profile
Issue Date 2012
Source Science China. Mathematics , v. 55, (11), 2012, p. 2347-2366
Summary Let a n, n ≥ 1 be a sequence of independent standard normal random variables. Consider the random trigonometric polynomial T n(θ) = Σ j=1 na j cos(jθ), 0 ≤ θ ≤ 2π and let N n be the number of real roots of T n(θ) in (0, 2π). In this paper it is proved that lim n → ∞ Var(N n)/n where 0 < c 0 < ∞. © 2012 Science China Press and Springer-Verlag Berlin Heidelberg.
Subjects
ISSN 1674-7283
Language English
Format Article
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