Palindromic random trigonometric polynomials

@article{Conrey2008PalindromicRT,
  title={Palindromic random trigonometric polynomials},
  author={J. Brian Conrey and David W. Farmer and Ozlem Imamoglu},
  journal={arXiv: Probability},
  year={2008}
}
We show that if a real trigonometric polynomial has few real roots, then the trigonometric polynomial obtained by writing the coefficients in reverse order must have many real roots. This is used to show that a class of random trigonometric polynomials has, on average, many real roots. In the case that the coefficients of a real trigonometric polynomial are independently and identically distributed, but with no other assumptions on the distribution, the expected fraction of real zeros is at… 
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Real zeros of random trigonometric polynomials with pairwise equal blocks of coefficients
  • Ali Pirhadi
  • Mathematics
    Rocky Mountain Journal of Mathematics
  • 2020
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.…

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