Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

DOI10.1016/j.jat.2006.03.006zbMath1127.47037arXivmath/0603098OpenAlexW1978323010MaRDI QIDQ2502877

Barry Simon, E. Brian Davies

Publication date: 13 September 2006

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603098

zbMATH Keywords

distribution of zeroseigenvalue estimatesrandom orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Eigenvalues, singular values, and eigenvectors (15A18) Stochastic processes (60G99) Random matrices (algebraic aspects) (15B52) Random linear operators (47B80)

Related Items

Sharp estimate on the resolvent of a finite-dimensional contraction, Maximum of the resolvent over matrices with given spectrum, Zero spacings of paraorthogonal polynomials on the unit circle, Anderson localization for the quasi-periodic CMV matrices with Verblunsky coefficients defined by the skew-shift, On orthogonal polynomials obtained via polynomial mappings, Lyapunov behavior and dynamical localization for quasi-periodic CMV matrices, A complete unitary similarity invariant for unicellular matrices, Zeros of non-Baxter paraorthogonal polynomials on the unit circle, Spectral variation bounds in hyperbolic geometry, A formula related to CMV matrices and Szegő cocycles, Szegő transformations and \(n\)th order associated polynomials on the unit circle, Eigenvalue estimates for the resolvent of a non-normal matrix, Sharpening a result by E. B. Davies and B. Simon, Poisson brackets of orthogonal polynomials, Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent, Asymptotics on the support for Sobolev orthogonal polynomials on a bounded interval

Uses Software

• Eigtool

Cites Work

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