Electronic Journal of Probability
- Electron. J. Probab.
- Volume 21 (2016), paper no. 73, 37 pp.
Large deviations for the empirical measure of random polynomials: revisit of the Zeitouni-Zelditch theorem
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