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The zeros of random polynomials cluster uniformly near the unit circle


Hughes, C P; Nikeghbali, A (2008). The zeros of random polynomials cluster uniformly near the unit circle. Compositio Mathematica, 144(3):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.

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.

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21 citations in Web of Science®
24 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:14 Jan 2009 14:13
Last Modified:05 Apr 2016 12:39
Publisher:London Mathematical Society
ISSN:0010-437X
Additional Information:Copyright: Cambridge University Press
Publisher DOI:https://doi.org/10.1112/S0010437X07003302
Related URLs:http://arxiv.org/abs/math/0406376

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