Related papers: An enhanced term in the Szeg\H{o}-type asymptotics…

We consider a multi-dimensional continuum Schr\"odinger operator $H$ which is given by a perturbation of the negative Laplacian by a compactly supported bounded potential. We show that, for a fairly large class of test functions, the…

We prove Szeg\H{o}-type trace asymptotics for translation-invariant operators on polygons. More precisely, consider a Fourier multiplier $A=\mathcal{F}^\ast \sigma \mathcal{F}$ on $\mathsf{L}^2(\mathbb{R}^2)$ with a sufficiently decaying,…

This article concerns the asymptotics of pseudodifferential operators whose Weyl symbol is the convolution of a discontinuous function dilated by a large scaling parameter with a smooth function of constant scale. These operators include as…

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…

We prove that the Szeg\H{o} function, $D(z)$, of a measure on the unit circle is entire meromorphic if and only if the Verblunsky coefficients have an asymptotic expansion in exponentials. We relate the positions of the poles of $D(z)^{-1}$…

The main result in this paper is a one term Szego type asymptotic formula with a sharp remainder estimate for a class of integral operators of the pseudodifferential type with symbols which are allowed to be non-smooth or discontinuous in…

We prove full Szeg\H{o}-type large-box trace asymptotics for selfadjoint $\mathbb{Z}^d$-ergodic operators $\Omega\ni \omega\mapsto H_\omega$ acting on $L^2(\mathbb{R}^d)$. More precisely, let $g$ be a bounded, compactly supported and…

In this paper we establish new integral representations for the remainder term of the known asymptotic expansion of the logarithm of the Barnes $G$-function. Using these representations, we obtain explicit and numerically computable error…

We prove a formula for the leading term of the asymptotic expansion of the holomorphic analytic torsion of the Dirac operator modified by the Clifford action of a real three-form.

We give an explicit formula for the logarithmic potential of the asymptotic zero-counting measure of the sequence $\left\{\frac{\mathrm{d}^n}{\mathrm{d}z^n}\left(R(z)\exp{T(z)}\right)\right\}$. Here, $R(z)$ is a rational function with at…

We give a complete rigorous proof of the full asymptotic expansion of the partition function of the dimer model on a square lattice on a torus for general weights $z_h, z_v$ of the dimer model and arbitrary dimensions of the lattice $m, n$.…

We consider an elliptic self-adjoint first order differential operator L acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of the operator L…

We consider an elliptic self-adjoint first order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of our operator is…

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 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 derive an asymptotic expansion for off-diagonal coherent-state matrix elements of non-polynomial operators in gauge theories admitting holomorphic coherent-state representations. The derivation combines stationary-phase analysis with an…

We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the…

We develop a theory of regularity for Dirac operators with uniformly locally square-integrable operator data. This is motivated by Stahl--Totik regularity for orthogonal polynomials and by recent developments for continuum Schr\"odinger…

We work out a generalization of the Szeg\"o limit theorems on the determinant of large matrices. We focus on matrices with nonzero leading principal minors and elements that decay to zero exponentially fast with the distance from the main…

We consider the asymptotics of the partition function of the extended Gross-Witten-Wadia unitary matrix model by introducing an extra logarithmic term in the potential. The partition function can be written as a Toeplitz determinant with…