# The minimum modulus of Gaussian trigonometric polynomials

```@article{Yakir2021TheMM,
title={The minimum modulus of Gaussian trigonometric polynomials},
author={Oren Yakir and Ofer Zeitouni},
journal={Israel Journal of Mathematics},
year={2021}
}```
• Published 16 June 2020
• Mathematics
• Israel Journal of Mathematics
We prove that the minimum of the modulus of a random trigonometric polynomial with Gaussian coefficients, properly normalized, has limiting exponential distribution.
4 Citations
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## References

SHOWING 1-10 OF 17 REFERENCES
On roots of random polynomials
• Mathematics
• 1997
We study the distribution of the complex roots of random polynomials of degree n with i.i.d. coefficients. Using techniques related to Rice’s treatment of the real roots question, we derive, under
On the Distribution of Roots of Random Polynomials
In the study of algebraic and numerical properties of polynomials one occasionally introduces the notion of a random polynomial. For example, this chapter was originally motivated by investigations,
The zeros of random polynomials cluster uniformly near the unit circle
• Mathematics
Compositio Mathematica
• 2008
Abstract In this paper we deduce a universal result about the asymptotic distribution of roots of random polynomials, which can be seen as a complement to an old and famous result of Erdős and Turan.
Lower bounds for the absolute value of random polynomials on a neighborhood of the unit circle
• Mathematics
• 1999
Abstract. Let T (x) = ∑n−1 j=0 ±eijx where ± stands for a random choice of sign with equal probability. The first author recently showed that for any > 0 and most choices of sign, minx∈[0,2π) |T (x)|
On the Distribution of Roots of Polynomials
• Mathematics
• 1950
1. We start by explaining two groups of theorems and we shall derive both from a common source. P. Bloch and G. P6lya' investigated first the question of giving an upper estimation of the number R of
Some Random Series of Functions
1. A few tools from probability theory 2. Random series in a Banach space 3. Random series in a Hilbert space 4. Random Taylor series 5. Random Fourier series 6. A bound for random trigonometric
The Complex Zeros of Random Polynomials
• Mathematics
• 1995
Mark Kac gave an explicit formula for the expectation of the number, vn (a), of zeros of a random polynomial, n-I Pn(z) = E ?tj, j=O in any measurablc subset Q of the reals. Here, ... ?In-I are
Normal Approximation and Asymptotic Expansions
• Mathematics
• 1976
Preface to the Classics Edition Preface 1. Weak convergence of probability measures and uniformity classes 2. Fourier transforms and expansions of characteristic functions 3. Bounds for errors of
Extreme Local Extrema of Two-Dimensional Discrete Gaussian Free Field
• Mathematics
• 2013
We consider the discrete Gaussian Free Field in a square box in \$\${\mathbb{Z}^2}\$\$Z2 of side length N with zero boundary conditions and study the joint law of its properly-centered extreme values (h)
Sur l’équation de convolution μ = μ ⋆ σ
• C. R. Acad. Sci. Paris Vol. 250, pp. 799–801
• 1960