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Large deviations for the empirical measure of random polynomials: revisit of the Zeitouni-Zelditch theorem. (English) Zbl 1354.60026
Summary: This article revisits the work by O. Zeitouni and S. Zelditch [Int. Math. Res. Not. 2010, No. 20, 3935–3992 (2010; Zbl 1206.60031)] 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.

60F10 Large deviations
Full Text: DOI Euclid