Palindromic random trigonometric polynomials
Probability
2008-12-10 v1 Complex Variables
Abstract
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 least one-half. This result is best possible.
Cite
@article{arxiv.0812.1752,
title = {Palindromic random trigonometric polynomials},
author = {J. Brian Conrey and David W. Farmer and Özlem Imamoglu},
journal= {arXiv preprint arXiv:0812.1752},
year = {2008}
}
Comments
5 pages. To appear in PAMS