Mean Number of Real Zeros of a Random Hyperbolic Polynomial

Abstract

Consider the random hyperbolic polynomial, f(x) = 1a1 coshx+···+np × an coshnx, in which n and p are integers such that n ≥ 2, p ≥ 0, and the coefficients ak(k = 1,2, . . . ,n) are independent, standard normally distributed random variables. If νnp is the mean number of real zeros of f(x), then we prove that νnp = π−1 logn+ O{(logn)1/2}. 

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Cite this paper

@inproceedings{Ernest2000MeanNO, title={Mean Number of Real Zeros of a Random Hyperbolic Polynomial}, author={J. Ernest}, year={2000} }