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Tue, Apr 17, 2018
Analysis Seminar
3:30 PM
MSCS 514
Random trigonometric polynomials with pairwise equal blocks of coefficients III
 Abstract: It is known that the expected number of real zeros of a random trigonometric polynomial $V_n(x) = \sum_ {j=0} ^{n} a_j \cos (jx)$ on $[0,2 \pi]$, where the coefficients $a_j$ are i.i.d. random variables with Gaussian distribution $\mathcal{N}(0,\sigma^2)$, is asymptotically equal to $2n/\sqrt{3}$. We define the $i$-th block of coefficients of length $L$ as $B_i= \left( a_{iL}, a_{iL+1}, \ldots , a_{iL+L-1} \right).$ In this series of talks, we investigate the expected number of real zeros of random trigonometric polynomials with palindromic blocks of coefficients, i.e., identical blocks positioned symmetrically in the list of coefficients.