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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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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Additional Information

Ildar Ibragimov
Affiliation: Mathematics Institute, Fontanka 27, St. Petersburg 191011, Russia
Email: ibr32@pdmi.ras.ru

Ofer Zeitouni
Affiliation: Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
Email: zeitouni@ee.technion.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01766-2
PII: S 0002-9947(97)01766-2
Keywords: Random polynomials, complex roots, domain of attraction of the stable law
Received by editor(s): December 2, 1995
Additional Notes: The work of the first author was partially supported by the Russian Foundation for Fundamental Research, grant 94-01-00301, and by grants R36000 and R36300 of the International Scientific Foundation.
The work of the second author was done while he visited MIT, under support from NSF grant 9302709–DMS
Article copyright: © Copyright 1997 American Mathematical Society