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 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:
https://doi.org/10.1090/S0002-9947-97-01766-2

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