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April, 1986 On the Average Number of Real Roots of a Random Algebraic Equation
Kambiz Farahmand
Ann. Probab. 14(2): 702-709 (April, 1986). DOI: 10.1214/aop/1176992539


There are many known asymptotic estimates of the expected number of zeros of a polynomial of degree $n$ with independent random coefficients, for $n \rightarrow \infty$. The present paper provides an estimate of the expected number of times that such a polynomial assumes the real value $K$, where $K$ is not necessarily zero. The coefficients are assumed to be normally distributed. It is shown that the results are valid even for $K \rightarrow \infty$, as long as $K = O(\sqrt n)$.


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Kambiz Farahmand. "On the Average Number of Real Roots of a Random Algebraic Equation." Ann. Probab. 14 (2) 702 - 709, April, 1986.


Published: April, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0694.60060
MathSciNet: MR832032
Digital Object Identifier: 10.1214/aop/1176992539

Keywords: 60H , Kac-Rice formula , Number of real roots , random algebraic equation

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 2 • April, 1986
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