Wenbo V. Li

Title: No chance for families of random polynomials to have all real roots

Co-Authors: Patrick Devlin and Mingyu Xu

Abstract: We study polynomials $f$ with coefficients from a given set $S$, such that $f$ has only real roots. We show that if $S$ satisfies some general conditions, which we make explicit, then the degree of $f$ is necessarily bounded. As a particular corollary of this, we show that if $f$ is viewed as a degree $n$ random polynomial, whose coefficients must lie in $S$, then the probability that it has all real roots is zero for all sufficiently large $n$.

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Last modified Oct. 10, 2010 by Wenbo V. Li,

wli@math.udel.edu