Nicholas Cook, Duke University, Universality for the minimum modulus of random trigonometric polynomials
ZoomWe consider the restriction to the unit circle of random degree-n polynomials with iid coefficients (Kac polynomials). Recent work of Yakir and Zeitouni shows that for Gaussian coefficients, the minimum modulus (suitably rescaled) follows a limiting exponential distribution. We show this is a universal phenomenon, extending their result to arbitrary sub-Gaussian coefficients, such as Rademacher…