On roots of random polynomials

И. А. Ибрагимов, Ofer Zeitouni

Type: Article

Publication Date: 1997-01-01

Citations: 100

DOI: https://doi.org/10.1090/s0002-9947-97-01766-2

Abstract

We study the distribution of the complex roots of random polynomials of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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.

Locations

Transactions of the American Mathematical Society - View - PDF

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