Publications [#360134] of Nicholas A Cook

Papers Published

1. Cook, NA; Nguyen, HH, Universality of the minimum modulus for random trigonometric polynomials, vol. 40 (January, 2021), pp. 46 pages, Discrete Analysis
   (last updated on 2024/04/24)

   Abstract:
   It has been shown in a recent work by Yakir-Zeitouni that the minimum modulus of random trigonometric polynomials with Gaussian coefficients has a limiting exponential distribution. We show this is a universal phenomenon. Our approach relates the joint distribution of small values of the polynomial at a fixed number $m$ of points on the circle to the distribution of a certain random walk in a $4m$-dimensional phase space. Under Diophantine approximation conditions on the angles, we obtain strong small ball estimates and a local central limit theorem for the distribution of the walk.