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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10}

**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*