%A Yu, Peihan
%D 2019
%T An Analog of the Salem-Zygmund Theorem for Orthogonal Polynomials on the Unit Circle
%K
%X In this note, I study the result and proof of the classical Salem-Zygmund Theorem. I apply the method to random orthogonal polynomials on the unit circle. The goal is to find the distribution of M , the sup norm of suitably defined random polynomial orthogonal on the unit circle. In my proof, I use Bernstein and Chebyshev inequalities to achieve this goal. I find that for fixed large κ, the probability of M > κ drops significantly as the degree n of the orthogonal polynomial grows.
%U https://mjum.math.umn.edu/index.php/mjum/article/view/58
%J Minnesota Journal of Undergraduate Mathematics
%0 Journal Article
%V 4
%N 1
%@ 2378-5810
%8 2019-02-04