Asymptotic behavior of roots of random polynomial equations
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- by Efraim Shmerling and Kenneth J. Hochberg PDF
- Proc. Amer. Math. Soc. 130 (2002), 2761-2770 Request permission
Abstract:
We derive several new results on the asymptotic behavior of the roots of random polynomial equations, including conditions under which the distributions of the zeros of certain random polynomials tend to the uniform distribution on the circumference of a circle centered at the origin. We also derive a probabilistic analog of the Cauchy-Hadamand theorem that enables us to obtain the radius of convergence of a random power series.References
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Additional Information
- Efraim Shmerling
- Affiliation: Department of Mathematics, College of Judea and Samaria, 44837 Ariel, Israel
- Kenneth J. Hochberg
- Affiliation: Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel
- Email: hochberg@macs.biu.ac.il
- Received by editor(s): November 11, 2000
- Received by editor(s) in revised form: March 23, 2001
- Published electronically: March 13, 2002
- Communicated by: Claudia M. Neuhauser
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2761-2770
- MSC (2000): Primary 60H25, 47B80, 34F05
- DOI: https://doi.org/10.1090/S0002-9939-02-06340-2
- MathSciNet review: 1900883