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

Raphael Butez

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arXiv · 1509.09136

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

Raphael Butez

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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.

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Raphael Butez. 2015-09-30. Large deviations for the empirical measure of random polynomials: revisit of the Zeitouni-Zelditch theorem. https://arxiv.org/abs/1509.09136

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