Sine kernel asymptotics for a class of singular measures

DOI10.1016/j.jat.2011.05.006zbMath1228.42028arXiv1011.3159OpenAlexW2060961100MaRDI QIDQ719504

Jonathan Breuer

Publication date: 10 October 2011

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

Full work available at URL: https://arxiv.org/abs/1011.3159

zbMATH Keywords

Christoffel-Darboux kernelsingular continuous measure

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Spaces of measures, convergence of measures (28A33)

Related Items (10)

An update on local universality limits for correlation functions generated by unitary ensembles ⋮ The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles ⋮ Level repulsion for Schrödinger operators with singular continuous spectrum ⋮ Spacing properties of the zeros of orthogonal polynomials on Cantor sets via a sequence of polynomial mappings ⋮ A universality theorem for ratios of random characteristic polynomials ⋮ On the spacing of zeros of paraorthogonal polynomials for singular measures ⋮ Two universality results for polynomial reproducing kernels ⋮ Stability of asymptotics of Christoffel-Darboux kernels ⋮ Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients ⋮ Universality for eigenvalue correlations from the unitary ensemble associated with a family of singular weights

Cites Work

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• Some recent methods for establishing universality limits
• Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum
• A new approach to universality limits involving orthogonal polynomials
• Two extensions of Lubinsky's universality theorem
• Universality for locally Szegő measures
• Universality limits in the bulk for arbitrary measures on compact sets
• Universality and fine zero spacing on general sets
• Géza Freud, orthogonal polynomials and Christoffel functions. A case study
• Singular continuous measures in scattering theory
• Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
• Applications of universality limits to zeros and reproducing kernels of orthogonal polynomials
• A class of orthogonal polynomials
• The Christoffel-Darboux Kernel

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