Ali Pirhadi

Oklahoma State University

Talk Title: Random trigonometric polynomials with pairwise equal blocks of coefficients

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 (0,2\pi) $, with the $ a_j $ being standard Gaussian i.i.d. random variables is asymptotically $ 2n / \sqrt{3} $. We investigate three different cases of random cosine polynomials with pairwise equal blocks of coefficients and show that in each case (asymptotically) $ \mathbb{E}[N_n (0,2\pi)] \gtrsim 2n / \sqrt{3}. $