Related papers: Asymptotic behaviour of Christoffel-Darboux kernel…
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…
Computing asymptotics of the recurrence coefficients of X1-Jacobi polynomials we investigate the limit of Christoffel function. We also study the relation between the normalized counting measure based on the zeros of the modified average…
We study the stability of convergence of the Christoffel-Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations…
We study weak asymptotic behaviour of the Christoffel--Darboux kernel on the main diagonal corresponding to multiple orthogonal polynomials. We show that under some hypotheses the weak limit of $\tfrac{1}{n} K_n(x,x)\, d\mu$ is the same as…
We study spectrum of finite truncations of unbounded Jacobi matrices with periodically modulated entries. In particular, we show that under some hypotheses a sequence of properly normalized eigenvalue counting measures converge vaguely to…
We construct a family of measures on $\bbR$ that are purely singular with respect to Lebesgue measure, and yet exhibit universal sine-kernel asymptotics in the bulk. The measures are best described via their Jacobi recursion coefficients:…
We study scaling limits of deterministic Jacobi matrices at a fixed point, $x_0$, and their connection to the scaling limits of the Christoffel-Darboux kernel at that point. We show that in the case that the orthogonal polynomials are…
We introduce from an analytic perspective Christoffel-Darboux kernels associated to bounded, tracial noncommutative distributions. We show that properly normalized traces, respectively norms, of evaluations of such kernels on finite…
We study a one-parameter family of probability measures on lozenge tilings of large regular hexagons that interpolates between the uniform measure on all possible tilings and a particular fully frozen tiling. The description of the…
We study Jacobi matrices with $N$-periodically modulated recurrence coefficients when the sequence of $N$-step transfer matrices is convergent to a non-trivial Jordan block. In particular, we describe asymptotic behavior of their…
We provide a new method to approximate a (possibly discontinuous) function using Christoffel-Darboux kernels. Our knowledge about the unknown multivariate function is in terms of finitely many moments of the Young measure supported on the…
We study solutions of three-term recurrence relations whose $N$-step transfer matrices belong to the uniform Stolz class. In particular, we derive the first order of their uniform asymptotics. For orthonormal polynomials we show more.…
We study the double scaling limit for unitary invariant ensembles of random matrices with non analytic potentials and find the asymptotic expansion for the entries of the corresponding Jacobi matrix. Our approach is based on the…
We present a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes a mass uniformly distributed on the sphere. First, connection formulas relating these multivariate orthogonal…
The Christoffel-Darboux kernels for orthogonal polynomials in several real variables are investigated within the context of the three term recurrence relation reformulated for this purpose. Examples of orthogonal polynomials on the unit…
We prove a version of strong asymptotics of Christoffel functions with varying weights for a general class of sets E and measures in the complex plane. This class includes all regular measures in the sense of Stahl-Totik on regular compact…
We give formulas for the density of the measure of orthogonality for orthonormal polynomials with unbounded recurrence coefficients. The formulas involve limits of appropriately scaled Tur\'an determinants or Christoffel functions. Exact…
We apply the new framework for modularity of false theta functions developed by the second author and Nazaroglu to study the asymptotic behavior of Taylor coefficients of false Jacobi forms. The examples we study generate moments of the…
Our goal is to find an asymptotic behavior as $n\to\infty$ of orthogonal polynomials $P_{n}(z)$ defined by the Jacobi recurrence coefficients $a_{n}, b_{n}$. We suppose that the off-diagonal coefficients $a_{n}$ grow so rapidly that the…
Two central objects in constructive approximation, the Christoffel-Darboux kernel and the Christoffel function, are encoding ample information about the associated moment data and ultimately about the possible generating measures. We…