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The Expected Number of Local Maxima of a Random Algebraic Polynomial

Authors:	K Farahmand P Hannigan

Abstract:	In this work we obtain an asymptotic estimate for the expected number of maxima of the random algebraic polynomial $a_0 + a_1 x + a_2 x^2 + \cdots + a_{n - 1} x^{n - 1}$ , where a _j (j=0, 1,...,n–1) are independent, normally distributed random variables with mean and variance one. It is shown that for nonzero , the expected number of maxima is asymptotic to $((\sqrt 3 + 1)/4\pi )$ log n, when n is large.

Keywords:	Gaussian process number of real roots Kac-Rice formula normal density covariance matrix random algebraic polynomial local maxima
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