Related papers: Relative Szeg\H{o} asymptotics for Toeplitz determ…

We study right limits of the Bergman Shift matrix. Our results have applications to ratio asymptotics, weak asymptotic measures, relative asymptotics, and zero counting measures of the orthogonal and orthonormal polynomials.

The authors of the title proved an elegant identity expressing a Toeplitz determinant in terms of the Fredholm determinant of an infinite matrix which (although not described as such) is the product of two Hankel matrices. The proof used…

We carry out the asymptotic analysis as $n \to \infty$ of a class of orthogonal polynomials $p_{n}(z)$ of degree $n$, defined with respect to the planar measure \begin{equation*} d\mu(z) = (1-|z|^{2})^{\alpha-1}|z-x|^{\gamma}\mathbf{1}_{|z|…

We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for…

We compute the limiting statistical distribution of the eigenvalues of sequences of matrices whose entries satisfy what we call a vanishing mean variation condition and are $\mu$-distributed for some probability measure. As an application…

We establish semiclassical asymptotics and estimates for the $e_h(x,x;\tau)$ where $e_h(x,y,\tau)$ is the Schwartz kernel of the spectral projector for a second order elliptic operator inside domain with power singularity in the origin.…

We study the behavior of weighted residual polynomials on circular arcs, including weighted Chebyshev polynomials. For weights given by reciprocals of polynomials, we establish Szeg\H{o}-Widom asymptotics. Extending our analysis to less…

We obtain Szeg\H o-type limit theorems for Toeplitz operators on the weighted Bergman spaces $A^{2}_{\alpha}(\mathbb{B}^{n})$, and on $L^{2}(G)$, presenting separate formulations for compact and locally compact Abelian groups. Furthermore,…

We consider a Jordan arc \Gamma in the complex plane \mathbb{C} and a regular measure \mu whose support is \Gamma . We denote by D the upper Hessenberg matrix of the multiplication by z operator with respect to the orthonormal polynomial…

In this survey we show how to produce asymptotics of determinants of structured matrices using operator theory methods. We describe the asymptotics for finite Toeplitz matrices, finite Toeplitz plus Hankel matrices and generalizations of…

We obtain Szeg\H{o}-type Limit Theorems in the setting of Reproducing Kernel Hilbert Spaces on discs in $\mathbb{C}$. From this, we derive a formula for the density of the eigenvalues of compressions of Toeplitz operators. Examples for the…

Let $A = (a_{j,k})_{j,k=-\infty}^\infty$ be a bounded linear operator on $l^2(\mathbb{Z})$ whose diagonals $D_n(A) = (a_{j,j-n})_{j=-\infty}^\infty\in l^\infty(\mathbb{Z})$ are almost periodic sequences. For certain classes of such…

We compute the leading and sub-leading terms in the asymptotic expansion of the Szeg\"o kernel on the diagonal of a class of pseudoconvex Reinhardt domains whose boundaries are endowed with a general class of smooth measures. We do so by…

We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…

In this paper it was proved that the quantum relative entropy $D(\sigma \| \rho)$ can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of POVMs. The sequence of POVMs depends on $\rho$,…

We establish semiclassical asymptotics and estimates for the Schwartz kernel $e_h(x,y;\tau)$ of spectral projector for a second order elliptic operator on the manifold with a boundary. While such asymptotics for its restriction to the…

Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that…

Let $X$ be an orbisurface, meaning a compact hyperbolic Riemann surface possibly with a finite number of elliptic points, and let $X_1$ denote its unit tangent bundle. We consider the twisted Selberg zeta function $Z(s;\rho)$ associated to…

We study the asymptotics of the natural $L^2$ metric on the Hitchin moduli space with group $G = \mathrm{SU}(2)$. Our main result, which addresses a detailed conjectural picture made by Gaiotto, Neitzke and Moore \cite{gmn13}, is that on…

We study the asymptotic behaviour of suitably defined seminorms in general metric measure spaces. As a particular case we provide new and shorter proofs of the Maz'ya-Shaposhnikova's theorem on the asymptotic behaviour of the fractional…