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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.
ISSN 1674-7283
Language English
Format Article
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