Expected number of real roots of random trigonometric polynomials

Hendrik Flasche

Stochastic Processes and their Applications, 2017, vol. 127, issue 12, 3928-3942

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).

Keywords: Zeros of random analytic functions; Random trigonometric polynomials; Functional limit theorem (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2017.03.018

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