On roots of random polynomials

Ibragimov, Ildar; Zeitouni, Ofer

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

On roots of random polynomials
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by Ildar Ibragimov and Ofer Zeitouni PDF

Trans. Amer. Math. Soc. 349 (1997), 2427-2441 Request permission

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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