The minimum modulus of Gaussian trigonometric polynomials

TL;DR

This paper proves that the normalized minimum modulus of Gaussian trigonometric polynomials follows a limiting exponential distribution, revealing a universal statistical behavior.

Contribution

It establishes the limiting distribution of the minimum modulus for Gaussian trigonometric polynomials, a novel result in the probabilistic analysis of such functions.

Findings

Minimum modulus follows exponential distribution asymptotically

Normalized minimum modulus converges in distribution

Provides new insights into Gaussian trigonometric polynomial behavior

Abstract

We prove that the minimum of the modulus of a random trigonometric polynomial with Gaussian coefficients, properly normalized, has limiting exponential distribution.