Asymptotic Behavior Of Polynomials Research Articles

Free Convolution Powers Via Roots of Polynomials

ABSTRACT Let μ be a compactly supported probability measure on the real line. Bercovici-Voiculescu and Nica-Speicher proved the existence of a free convolution power for any real . The purpose of this short note is to give a formal proof of an elementary description of in terms of polynomials and roots of their derivatives. This bridge allows us to switch back and forth between free probability and the asymptotic behavior of polynomials.

Asymptotic analysis of the density of states in random matrix models associated with a slowly decaying weight

The asymptotic behavior of polynomials that are orthogonal with respect to a slowly decaying weight is very different from the asymptotic behavior of polynomials that are orthogonal with respect to a Freud-type weight. While the latter has been extensively studied, much less is known about the former. Following an earlier investigation into the zero behavior, we study here the asymptotics of the density of states in a unitary ensemble of random matrices with a slowly decaying weight. This measure is also naturally connected with the orthogonal polynomials. It is shown that, after suitable rescaling, the weak limit is the same as the weak limit of the rescaled zeros.

The geometry of the asymptotics of polynomial maps

The aim of this paper is to develop a theory for the asymptotic behavior of polynomials and of polynomial maps overR and overC and to apply it to the Jacobian conjecture. This theory gives a unified frame for some results on polynomial maps that were not related before.

On the asymptotic behavior of polynomials with extremal properties, and of their zeros

On the asymptotic behavior of polynomials with extremal properties, and of their zeros