Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II

Abstract

We study orthogonal polynomials with periodically modulated Jacobi parameters in the case when $0$ lies on the soft edge of the spectrum of the corresponding periodic Jacobi matrix. We determine when the orthogonality measure is absolutely continuous and we provide a constructive formula for it in terms of the limit of Turán determinants. We next consider asymptotics of the solutions of associated second order difference equation. Finally, we study scaling limits of the Christoffel--Darboux kernel.

40 pages

References in corpus (6)

• Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case
• An example of spectral phase transition phenomenon in a class of Jacobi matrices with periodically modulated weights
• About essential spectra of unbounded Jacobi matrices
• Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation I
• Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case II
• Asymptotic behavior of orthogonal polynomials. Singular critical case

Cited by in corpus (7)

• About essential spectra of unbounded Jacobi matrices
• Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation I
• Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case II
• Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case
• Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients
• Universality for random matrices with equi-spaced external source: a case study of a biorthogonal ensemble
• Nevai's condition for measures with unbounded supports