相关论文: Asymptotics for Toeplitz determinants on a circula…
A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of…
In the theory of the two-dimensional Ising model, the diagonal susceptibility is equal to a sum involving Toeplitz determinants. In terms of a parameter k the diagonal susceptibility is analytic inside the unit circle, and the authors…
We prove a higher order asymptotic formula for traces of finite block Toeplitz matrices with symbols belonging to H\"older-Zygmund spaces. The remainder in this formula goes to zero very rapidly for very smooth symbols. This formula refine…
We investigate the asymptotics of the determinant of N by N Hankel matrices generated by Fisher-Hartwig symbols defined on the real line, as N becomes large. Such objects are natural analogues of Toeplitz determinants generated by…
Motivated by the recent results on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities, we develop an asymptotic expansion for transverse spin correlations in the XX spin-1/2 chain. The coefficients of the…
We prove higher order asymptotic formulas for determinants and traces of finite block Toeplitz matrices generated by matrix functions belonging to generalized H\"older spaces with characteristic functions from the Bari-Stechkin class. We…
We review the asymptotic behavior of a class of Toeplitz (as well as related Hankel and Toeplitz + Hankel) determinants which arise in integrable models and other contexts. We discuss Szego, Fisher-Hartwig asymptotics, and how a transition…
Suppose that $\phi$ and $\psi$ are smooth complex-valued functions on the circle that are invertible, have winding number zero with respect to the origin, and have meromorphic extensions to an open neighborhood of the closed unit disk. Let…
In this paper we consider an interval $[\theta\_{1}, \theta\_{2}] \subset [0, \pi]$ and $f$ a differentiable, periodic and even function sufficiently smooth such that $f(\theta) \in [f(\theta\_{1}, f(\theta\_{2})] \iff \theta \in…
Muttalib-Borodin determinants are generalizations of Hankel determinants and depend on a parameter $\theta>0$. In this paper, we obtain large $n$ asymptotics for $n \times n$ Muttalib-Borodin determinants whose weight possesses an arbitrary…
By using Riemann--Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants $\det_N\big[ c_{\ell_a-m_b}[f] \big]$ generated by holomorhpic symbols, where $\ell_a=a$ (resp. $m_b=b$) except for a…
Asymptotically, we analytically derive the form of eigenvectors for two Fisher-Hartwig symbols besides those which were previously investigated in a $2016$ work due to Movassagh and Kadanoff, in which the authors characterized the…
Any sequence of uniformly bounded $N\times N$ Hermitian Toeplitz matrices $\{\boldsymbol{H}_N\}$ is asymptotically equivalent to a certain sequence of $N\times N$ circulant matrices $\{\boldsymbol{C}_N\}$ derived from the Toeplitz matrices…
Applying standard techniques from Toeplitz operator theory, we analyze the asymptotics of the Hilbert-Smith norms of the TQFT operators coming from isotopy classes of one dimensional oriented submanifolds on a closed oriented surface. We…
In this article, we determine the spectrum of real-analytic, non self-adjoint Toeplitz operators on compact K{\"a}hler manifolds and on the complex plane, on neighbourhoods of critical values of the symbol. We consider specifically critical…
In this article, we continue the development of the Riemann-Hilbert formalism for studying the asymptotics of Toeplitz+Hankel determinants with non-identical symbols, which we initiated in \cite{GI}. In \cite{GI}, we showed that the…
We present two elementary derivations of the formula for the Toeplitz determinant generated by a pure Fisher-Hartwig singularity.
In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in…
Sharp upper and lower bounds for the second and third order Hermitian-Toepilitz determinants are obtained for some generalized subclasses of starlike and convex functions. Applications of these results are also discussed for several widely…
We study the asymptotic behavior, as $n\to\infty$, of ratios of Toeplitz determinants $D_n(e^h d\mu)/D_n(d\mu)$ defined by a measure $\mu$ on the unit circle and a sufficiently smooth function $h$. The approach we follow is based on the…