 Tue, Apr 17, 2018

Analysis Seminar 3:30 PM MSCS 514  Random trigonometric polynomials with pairwise equal blocks of coefficients III Ali Pirhadi, OSU
  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 $B_i= \left( a_{iL}, a_{iL+1}, \ldots , a_{iL+L1} \right).$ 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. 


