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- W2947536259 abstract "It is well known that the expected number of real zeros of a random cosine polynomial $ V_n(x) = sum_ {j=0} ^{n} a_j cos (j x) , x in (0,2pi) $, with the $ a_j $ being standard Gaussian i.i.d. random variables is asymptotically $ 2n / sqrt{3} $. On the other hand, some of the previous works on the random cosine polynomials with dependent coefficients show that such polynomials have at least $ 2n / sqrt{3} $ expected real zeros lying in one period. In this paper we investigate two classes of random cosine polynomials with pairwise equal blocks of coefficients. First, we prove that a random cosine polynomial with the blocks of coefficients being of a fixed length and satisfying $ A_{2j}=A_{2j+1} $ possesses the same expected real zeros as the classical case. Afterwards, we study a case containing only two equal blocks of coefficients, and show that in this case significantly more real zeros should be expected compared to those of the classical case." @default.
- W2947536259 created "2019-06-07" @default.
- W2947536259 creator A5009383123 @default.
- W2947536259 date "2019-05-30" @default.
- W2947536259 modified "2023-09-27" @default.
- W2947536259 title "Real zeros of random trigonometric polynomials with pairwise equal blocks of coefficients" @default.
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