ar X iv : m at h / 07 02 36 0 v 1 [ m at h . N A ] 1 3 Fe b 20 07 On the number of minima of a random polynomial ∗
نویسندگان
چکیده
We give an upper bound in O(d) for the number of critical points of a normal random polynomial. The number of minima (resp. maxima) is in O(d)Pn, where Pn is the (unknown) measure of the set of symmetric positive matrices in the Gaussian Orthogonal Ensemble GOE(n). Finally, we give a closed form expression for the number of maxima (resp. minima) of a random univariate polynomial, in terms of hypergeometric functions.
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