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- W4287365438 abstract "In this paper, we quantify the rate of convergence between the distribution of number of zeros of random trigonometric polynomials (RTP) with i.i.d. centered random coefficients and the number of zeros of a stationary centered Gaussian process G, whose covariance function is given by the sinc function. First, we find the convergence of the RTP towards G in the Wasserstein-1 distance, which in turn is a consequence of Donsker Theorem. Then, we use this result to derive the rate of convergence between their respective number of zeros. Since the number of real zeros of the RTP is not a continuous function, we use the Kac-Rice formula to express it as the limit of an integral and, in this way, we approximate it by locally Lipschitz continuous functions." @default.
- W4287365438 created "2022-07-25" @default.
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- W4287365438 date "2021-01-28" @default.
- W4287365438 modified "2023-10-16" @default.
- W4287365438 title "Rates of convergence for the number of zeros of random trigonometric polynomials" @default.
- W4287365438 doi "https://doi.org/10.48550/arxiv.2101.12386" @default.
- W4287365438 hasPublicationYear "2021" @default.
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