TY - JOUR
AU - Yu, Peihan
PY - 2019/02/04
TI - An Analog of the Salem-Zygmund Theorem for Orthogonal Polynomials on the Unit Circle
JF - Minnesota Journal of Undergraduate Mathematics; Vol 4 No 1
KW -
N2 - 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.
UR - https://mjum.math.umn.edu/index.php/mjum/article/view/58