Asymptotic behavior of roots of random polynomial equations

Efraim Shmerling, Kenneth J. Hochberg

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish
Pages (from-to)2761-2770
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number9
StatePublished - Sep 2002


  • Random polynomials


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