Universal large deviations for Kac polynomials. (English) Zbl 1357.60029

Butez, Raphaël; Zeitouni, Ofer

Electron. Commun. Probab. 22, Paper No. 6, 10 p. (2017).

Summary: We prove the universality of the large deviations principle for the empirical measures of zeros of random polynomials whose coefficients are i.i.d. random variables possessing a density with respect to the Lebesgue measure on \(\mathbb{C}\), \(\mathbb{R}\) or \(\mathbb{R}^+\), under the assumption that the density does not vanish too fast at zero and decays at least as \(\exp -|x|^{\rho}\), \(\rho >0\), at infinity.

MSC:

60F10

Large deviations

Keywords:

large deviations; random polynomials