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}
}
We prove that the minimum of the modulus of a random trigonometric polynomial with Gaussian coefficients, properly normalized, has limiting exponential distribution. 
View With Semantic Reader
4 Citations
Background Citations
3

4 Citations

Citation Type

Citation Type

Universality of the minimum modulus for random trigonometric polynomials
Universality of the minimum modulus for random trigonometric polynomials, Discrete Analysis 2021:20, 46 pp. This paper belongs to a long tradition of study of the behaviour of random polynomials…
Universality of Poisson limits for moduli of roots of Kac polynomials
We give a new proof of a recent resolution [18] by Michelen and Sahasrabudhe of a conjecture of Shepp and Vanderbei [19] that the moduli of roots of Gaussian Kac polynomials of degree n, centered at…
The asymptotic joint distribution of the largest and the smallest singular values for random circulant matrices
In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent…
The asymptotic distribution of the condition number for random circulant matrices
. In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent…

References

SHOWING 1-10 OF 17 REFERENCES
On roots of random polynomials
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
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
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
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
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
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
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
...
...