On roots of random polynomials

Ibragimov, Ildar; Zeitouni, Ofer

doi:10.1090/S0002-9947-97-01766-2

On roots of random polynomials

Authors: Ildar Ibragimov and Ofer Zeitouni
Journal: Trans. Amer. Math. Soc. 349 (1997), 2427-2441
MSC (1991): Primary 34F05.; Secondary 26C10, 30B20
DOI: https://doi.org/10.1090/S0002-9947-97-01766-2
MathSciNet review: 1390040
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Abstract: We study the distribution of the complex roots of random polynomials of degree $n$ with i.i.d. coefficients. Using techniques related to Rice's treatment of the real roots question, we derive, under appropriate moment and regularity conditions, an exact formula for the average density of this distribution, which yields appropriate limit average densities. Further, using a different technique, we prove limit distribution results for coefficients in the domain of attraction of the stable law.

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