The minimum modulus of Gaussian trigonometric polynomials
Probability
2020-09-25 v2
Abstract
We prove that the minimum of the modulus of a random trigonometric polynomial with Gaussian coefficients, properly normalized, has limiting exponential distribution.
Keywords
Cite
@article{arxiv.2006.08943,
title = {The minimum modulus of Gaussian trigonometric polynomials},
author = {Oren Yakir and Ofer Zeitouni},
journal= {arXiv preprint arXiv:2006.08943},
year = {2020}
}
Comments
18 pages, 1 figure. Added a discussion on the method and a possible extension. To appear in the Israel Journal of Mathematics