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math.CA2018
An asymptotic expansion for the expected number of real zeros of real random polynomials spanned by OPUC
Hanan Aljubran, Maxim L. Yattselev
Let be a sequence of orthonormal polynomials on the unit circle with respect to a positive Borel measure that is symmetric with respect to conjugation…
math.CA2018
Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials
Alexander I. Aptekarev, Sergey A. Denisov, Maxim L. Yattselev
We consider a set of measures on the real line and the corresponding system of multiple orthogonal polynomials (MOPs) of the first and second type. Under some very mild assumptions…
math.CA2018
The reciprocal Mahler ensembles of random polynomials
Christopher D. Sinclair, Maxim L. Yattselev
We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree whose Mahler measure is bounded by a constant. After a change of variables this redu…