Universality of the minimum modulus for random trigonometric polynomials
Publication
, Journal Article
Cook, NA; Nguyen, HH
January 18, 2021
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.
Duke Scholars
Publication Date
January 18, 2021
Related Subject Headings
- Industrial Engineering & Automation
- Applied Mathematics
- 0913 Mechanical Engineering
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics
Citation
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Cook, N. A., & Nguyen, H. H. (2021). Universality of the minimum modulus for random trigonometric polynomials.
Cook, Nicholas A., and Hoi H. Nguyen. “Universality of the minimum modulus for random trigonometric polynomials,” January 18, 2021.
Cook NA, Nguyen HH. Universality of the minimum modulus for random trigonometric polynomials. 2021 Jan 18;
Cook, Nicholas A., and Hoi H. Nguyen. Universality of the minimum modulus for random trigonometric polynomials. Jan. 2021.
Cook NA, Nguyen HH. Universality of the minimum modulus for random trigonometric polynomials. 2021 Jan 18;
Publication Date
January 18, 2021
Related Subject Headings
- Industrial Engineering & Automation
- Applied Mathematics
- 0913 Mechanical Engineering
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics