The zeros of random polynomials cluster uniformly near the unit circle

Title	The zeros of random polynomials cluster uniformly near the unit circle
Publication Type	Journal Article
Year of Publication	2008
Authors	Hughes C, Nikeghbali A
Journal	Compositio Mathematica
Volume	144
Pagination	734--746
Abstract	In this paper we deduce a universal result about the asymptotic distribution of roots of random polynomials, which can be seen as a complement to an old and famous result of Erdos and Turan. More precisely, 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. The method we use is deterministic: in particular, we do not assume independence or equidistribution of the coefficients of the polynomial.
URL	http://arxiv.org/abs/math.CV/0406376
DOI	doi: 10.1112/S0010437X07003302
E-print number	arXiv:math.CV/0406376

Department of Mathematics