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Expected number of real roots of random trigonometric polynomials

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  • Flasche, Hendrik

Abstract

We investigate the asymptotics of the expected number of real roots of random trigonometric polynomials Xn(t)=u+1n∑k=1n(Akcos(kt)+Bksin(kt)),t∈[0,2π],u∈R whose coefficients Ak,Bk, k∈N, are independent identically distributed random variables with zero mean and unit variance. If Nn[a,b] denotes the number of real roots of Xn in an interval [a,b]⊆[0,2π], we prove that limn→∞ENn[a,b]n=b−aπ3exp(−u22).

Suggested Citation

  • Flasche, Hendrik, 2017. "Expected number of real roots of random trigonometric polynomials," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3928-3942.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:12:p:3928-3942
    DOI: 10.1016/j.spa.2017.03.018
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    Cited by:

    1. Hendrik Flasche & Zakhar Kabluchko, 2020. "Real Zeroes of Random Analytic Functions Associated with Geometries of Constant Curvature," Journal of Theoretical Probability, Springer, vol. 33(1), pages 103-133, March.

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