Universal large deviations for Kac polynomials

2016/07/08 by Raphaël Butez, Butez, Raphaël, Ofer Zeitouni +1
Mathematics · Economics, Econometrics and Finance · #Geometry and complex manifolds #Stochastic processes and statistical mechanics #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1607.02392

Abstract

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 C, R or R + , under the assumption that the density does not vanish too fast at zero and decays at least as exp --|x| ρ , ρ \textgreater 0, at infinity.

Related

• Large deviations for zeros of random polynomials with i.i.d. exponential coefficients
• Large deviations for the empirical measure of random polynomials:\n revisit of the Zeitouni-Zelditch theorem
• The largest root of random Kac polynomials is heavy tailed
• Large deviation theorem for zeros of polynomials and Hermitian random\n matrices
• Extreme value statistics for the roots of a complex Kac polynomial