Statistics Papers

Document Type

Journal Article

Date of this Version

2011

Publication Source

Theory of Probability & Its Applications

Volume

55

Issue

1

Start Page

173

Last Page

181

DOI

10.1137/S0040585X97984735

Abstract

We show that the expected number of real zeros of the nth degree polynomial with real independent identically distributed coefficients with common characteristic function φ(z) = e-A(ln|1/z|)^-a for 0 < |z| < 1 and φ(0) = 1, φ(z) ≡ 0 for 1 ≦ |z| < ∞, with 1 < a and A ≧ a(a-1), is (a-1)/(a-1/2) log(n) asymptotically as n → ∞.

Copyright/Permission Statement

Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Keywords

random polynomials, number of real zeros, real roots, Kac-Rice formula, characteristic function

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Date Posted: 27 November 2017

This document has been peer reviewed.