TY - JOUR

T1 - On the distribution of complex roots of random polynomials with heavy-tailed coefficients

AU - Götze, F.

AU - Zaporozhets, D.

PY - 2012/12/1

Y1 - 2012/12/1

N2 - Consider a random polynomial Gn(z) = ξnzn + · · · + ξ1 z + ξ0 with independent identically distributed complex-valued coefficients. Suppose that the distribution of log(1 + log(1 + |ξ0|)) has a slowly varying tail. Then the distribution of the complex roots of Gn concentrates in probability, as n → ∞, to two centered circles and is uniform in the argument as n → ∞. The radii of the circles are |ξ0/ξτ |1/τ and |ξτ /ξn |1/(n-τ), where ξτ denotes the coefficient with the maximum modulus. © 2012 Society for Industrial and Applied Mathematics.

AB - Consider a random polynomial Gn(z) = ξnzn + · · · + ξ1 z + ξ0 with independent identically distributed complex-valued coefficients. Suppose that the distribution of log(1 + log(1 + |ξ0|)) has a slowly varying tail. Then the distribution of the complex roots of Gn concentrates in probability, as n → ∞, to two centered circles and is uniform in the argument as n → ∞. The radii of the circles are |ξ0/ξτ |1/τ and |ξτ /ξn |1/(n-τ), where ξτ denotes the coefficient with the maximum modulus. © 2012 Society for Industrial and Applied Mathematics.

KW - Heavy-tailed coefficients

KW - Roots concentration

KW - Roots of a random polynomial

UR - http://www.scopus.com/inward/record.url?scp=84873678359&partnerID=8YFLogxK

U2 - 10.1137/S0040585X9798573X

DO - 10.1137/S0040585X9798573X

M3 - Article

AN - SCOPUS:84873678359

VL - 56

SP - 696

EP - 703

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 4

ER -