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 μ and variance one. It is shown that for nonzero μ, the expected number of maxima is asymptotic to \(((\sqrt 3 + 1)/4\pi )\)log n, when n is large.
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Farahmand, K., Hannigan, P. The Expected Number of Local Maxima of a Random Algebraic Polynomial. Journal of Theoretical Probability 10, 991–1002 (1997). https://doi.org/10.1023/A:1022618801587
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DOI: https://doi.org/10.1023/A:1022618801587