Mean number of real zeros of a random hyperbolic polynomial

J. Ernest Wilkins

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-8

Abstract:

Consider the random hyperbolic polynomial, f ( x ) = 1 p a 1 cosh x + ⋯ + n p × a n cosh n x , in which n and p are integers such that n ≥ 2 , p ≥ 0 , and the coefficients a k ( k = 1 , 2 , … , n ) are independent, standard normally distributed random variables. If ν n p is the mean number of real zeros of f ( x ) , then we prove that ν n p = π − 1 log n + O { ( log n ) 1 / 2 } .

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:605012

DOI: 10.1155/S0161171200001848

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