Geodesic
Universality of the minimum modulus for random trigonometric polynomials
Discrete analysis (2021) Cet article a éte moissonné depuis la source Scholastica

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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.
Publié le : 
@article{DAS_2021_a6,
     author = {Nicholas A. Cook and Hoi H. Nguyen},
     title = {Universality of the minimum modulus for random trigonometric polynomials},
     journal = {Discrete analysis},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2021_a6/}
}
TY  - JOUR
AU  - Nicholas A. Cook
AU  - Hoi H. Nguyen
TI  - Universality of the minimum modulus for random trigonometric polynomials
JO  - Discrete analysis
PY  - 2021
UR  - http://geodesic.mathdoc.fr/item/DAS_2021_a6/
LA  - en
ID  - DAS_2021_a6
ER  - 
%0 Journal Article
%A Nicholas A. Cook
%A Hoi H. Nguyen
%T Universality of the minimum modulus for random trigonometric polynomials
%J Discrete analysis
%D 2021
%U http://geodesic.mathdoc.fr/item/DAS_2021_a6/
%G en
%F DAS_2021_a6
Nicholas A. Cook; Hoi H. Nguyen. Universality of the minimum modulus for random trigonometric polynomials. Discrete analysis (2021). http://geodesic.mathdoc.fr/item/DAS_2021_a6/