## Electronic Journal of Probability

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

Raphaël Butez

#### 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
Accepted: 23 July 2016
First available in Project Euclid: 7 December 2016

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

#### 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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