Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

The zeros of random polynomials cluster uniformly near the unit circle

Auteur(s):

Code(s) de Classification MSC:

Résumé: Given a sequence of random polynomials, we show that, under some very general conditions, the roots tend to cluster near the unit circle, and their angles are uniformly distributed. In particular, we do not assume independence or equidistribution of the coefficients of the polynomial. We apply this result to various problems in both random and deterministic sequences of polynomials, including some problems in random matrix theory.

Mots Clés: Clustering of zeros ; Random polynomials

Date: 2004-06-21

Prépublication numéro: PMA-922