Electronic Journal of Probability

Large deviations for the empirical measure of random polynomials: revisit of the Zeitouni-Zelditch theorem

Raphaël Butez

Full-text: Open access

Abstract

This article revisits the work by Ofer Zeitouni and Steve Zelditch on large deviations for the empirical measures of random orthogonal polynomials with i.i.d. Gaussian complex coefficients, and extends this result to real Gaussian coefficients. This article does not require any knowledge in geometry. For clarity, we focus on two classical cases: Kac polynomials and elliptic polynomials.

Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 73, 37 pp.

Dates
Received: 15 February 2016
Accepted: 23 July 2016
First available in Project Euclid: 7 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1481079628

Digital Object Identifier
doi:10.1214/16-EJP5

Mathematical Reviews number (MathSciNet)
MR3592204

Zentralblatt MATH identifier
1354.60026

Subjects
Primary: 60F10: Large deviations

Keywords
random polynomials large deviations Coulomb gases

Rights
Creative Commons Attribution 4.0 International License.

Citation

Butez, Raphaël. Large deviations for the empirical measure of random polynomials: revisit of the Zeitouni-Zelditch theorem. Electron. J. Probab. 21 (2016), paper no. 73, 37 pp. doi:10.1214/16-EJP5. https://projecteuclid.org/euclid.ejp/1481079628


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