Related papers: Strong Szeg\H{o} Limit Theorems for Multi-Bordered…
Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz matrices. We…
We establish versions of Szeg\H{o}'s distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear…
Truncated Toeplitz operators are compressions of multiplication operators on $L^2$ to model spaces (that is, subspaces of $H^2$ which are invariant with respect to the backward shift). For this class of operators we prove certain Szeg\"o…
We compute the asymptotics of a block Toeplitz determinant which arises in the classical dimer model for the triangular lattice when considering the monomer-monomer correlation function. The model depends on a parameter interpolating…
In this work, we investigate quantitative properties of correlation functions on the boundaries between two 2D Ising-like models with dual parameters $\beta$ and $\beta^{\star}$. Spin-spin correlators in such constructions without…
We consider Berezin-Toeplitz operators whose multipliers are compactly supported densities carried by a submanifold of ${\mathbb C}^N$ . We compute asymptotically the moments of their spectral measures, and we prove Szeg\"o limit theorems…
The paper is a continuation of work [15] in which the general setting for analogs of the Szeg\"o theorem for ergodic operators was given and several interesting cases were considered. Here we extend the results of [15] to a wider class of…
In this paper, we study Toeplitz operators on generalized flag manifolds of compact Lie groups using a representation-theoretic point of view. We prove several basic properties of these Toeplitz operators, including an abstract formula for…
We derive closed-form asymptotic formulas for the R\'enyi entanglement entropies of the open XX spin-$1/2$ chain by mapping the underlying determinant of the boundary correlation matrix (which has Toeplitz-plus-Hankel structure) to a Hankel…
We give a survey on generalized Krein algebras $K_{p,q}^{\alpha,\beta}$ and their applications to Toeplitz determinants. Our methods originated in a paper by Mark Krein of 1966, where he showed that $K_{2,2}^{1/2,1/2}$ is a Banach algebra.…
We formulate and establish a noncommutative version of the well known Helson-Szego theorem about the angle between past and future for subdiagonal subalgebras. We then proceed to use this theorem to characterise the symbols of invertible…
In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of $n$ definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the…
We consider the determinantal point processes associated with the spectral projectors of a Schr\"odinger operator on $\mathbb{R}$, with a smooth confining potential. In the semiclassical limit, where the number of particles tends to…
The first Szego limit theorem has been extended by Bump-Diaconis and Tracy-Widom to limits of other minors of Toeplitz matrices. We extend their results still further to allow more general measures and more general determinants. We also…
In this paper, we revisit the problem of classifying real algebraic and semialgebraic sets by their topological types, focusing on establishing the effectiveness of bounds rather than deriving new quantitative estimates. Building on Hardt's…
In this paper, concerning SDEs with H\"older continuous drifts, which are merely dissipative at infinity, and SDEs with piecewise continuous drifts, we investigate the strong law of large numbers and the central limit theorem for underlying…
Complex systems can be effectively modeled via graphs that encode networked interactions, where relations between entities or nodes are often quantified by signed edge weights, e.g., promotion/inhibition in gene regulatory networks, or…
Let $\fre\subset\bbR$ be a finite union of disjoint closed intervals. We study measures whose essential support is $\fre$ and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szeg\H{o} condition is equivalent to \[…
We consider certain determinants with respect to a sufficiently regular Jordan curve $\gamma$ in the complex plane that generalize Toeplitz determinants which are obtained when the curve is the circle. This also corresponds to studying a…
A classical result by R. Rochberg says that every bounded Toeplitz operator $T$ on the Hilbert Paley-Wiener space $\mathrm{PW}_a^2$ admits a bounded symbol $\varphi$. We generalize this result to Toeplitz operators on the Banach…