Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case
arXiv:2008.07296 · doi:10.5802/aif.3624
Abstract
We study orthogonal polynomials with periodically modulated recurrence coefficients when lies on the hard edge of the spectrum of the corresponding periodic Jacobi matrix. In particular, we show that their orthogonality measure is purely absolutely continuous on a real half-line and purely discrete on its complement. Additionally, we provide the constructive formula for the density in terms of Turán determinants. Moreover, we determine the exact asymptotic behavior of the orthogonal polynomials. Finally, we study scaling limits of the Christoffel-Darboux kernel.
arXiv comment56 pages, 1 figure. It will appear at Annales de l'Institut Fourier
References in corpus (14)
- Orthogonal polynomial ensembles in probability theory
- Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble
- Properties of Generalized Freud Polynomials
- Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case
- Periodic perturbations of unbounded Jacobi matrices II: Formulas for density
- An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles
- Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors
- Periodic perturbations of unbounded Jacobi matrices III: The soft edge regime
- An example of spectral phase transition phenomenon in a class of Jacobi matrices with periodically modulated weights
- Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients
- About essential spectra of unbounded Jacobi matrices
- Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II
- Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation I
- Asymptotic behavior of orthogonal polynomials. Singular critical case