Real zeros of random trigonometric polynomials with dependent coefficients

Autor: Angst, Jürgen, Pautrel, Thibault, Poly, Guillaume

We further investigate the relations between the large degree asymptotics of the number of real zeros of random trigonometric polynomials with dependent coefficients and the underlying correlation function. We consider trigonometric polynomials of th

Externí odkaz: http://arxiv.org/abs/2102.09653

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New asymptotics for the mean number of zeros of random trigonometric polynomials with strongly dependent Gaussian coefficients

Autor: Pautrel Thibault

Publikováno v: Electron. Commun. Probab.
Electronic Communications in Probability
Electronic Communications in Probability, 2020, 25, paper no. 36, 13 pp. ⟨10.1214/20-ECP314⟩
Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2020, 25, paper no. 36, 13 pp. ⟨10.1214/20-ECP314⟩

We consider random trigonometric polynomials of the form \[ f_n(t):=\frac{1}{\sqrt{n}} \sum_{k=1}^{n}a_k \cos(k t)+b_k \sin(k t), \] where $(a_k)_{k\geq 1}$ and $(b_k)_{k\geq 1}$ are two independent stationary Gaussian processes with the same correla

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6be5e08292ec47822857b0933c332749