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

Raphael Butez (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Coulomb gases; Random polynomials; Large deviations

Domaines: Probabilités [math.PR]

Raphael Butez. Large deviations for the empirical measure of random polynomials: revisit of the Zeitouni-Zelditch theorem.. Electronic Journal of Probability, 2016, ⟨10.1214/16-EJP5⟩. ⟨hal-01206806v2⟩