On the Distribution of Roots of Random Polynomials

In the study of algebraic and numerical properties of polynomials one occasionally introduces the notion of a random polynomial. For example, this chapter was originally motivated by investigations, including [Ki, Re, SS, Sml, Sm2], into the complexity of root-finding algorithms for polynomials. We restrict our attention to central normal measures on spaces of polynomials, i.e., we assume that the coefficients of the polynomials have a multivariate normal distribution with mean zero and known covariance.

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