Abstract We study the averages of multiplicative eigenvalue statistics in ensembles orthogonal Haar-distributed matrices, which can alternatively be written as Toeplitz+Hankel determinants. obtain new asymptotics for symbols with Fisher–Hartwig singularities cases where some merge together and a gap or an emerging gap. these by relying on known analogous results unitary group associated polynom...

We prove the analogue of strong Szegő limit theorem for a large class bordered Toeplitz determinants. In particular, by applying our results to formula Au-Yang and Perk (Physica A 144:44–104, 1987) next-to-diagonal correlations $$\langle \sigma _{0,0}\sigma _{N-1,N} \rangle $$ in square lattice Ising model, we rigorously justify that long-range order is same as diagonal horizontal ones low temp...

The general form of Taylor's theorem gives the formula, f = P n + R n , where P n is the New-ton's interpolating polynomial, computed with respect to a connuent vector of nodes, and R n is the remainder. When f 0 6 = 0, for each m = 2; : : :; n + 1, we describe a \determinantal interpolation formula", f = P m;n +R m;n , where P m;n is a rational function in x and f itself. These formulas play a...

In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space H Cn of the unit circle. Firstly, we establish a tractable and explicit criterion on the hyponormality of block Toeplitz operators having bounded type symbols via the triangularization theorem for compressions of the shift operator. Secondly, we consider the gap...

It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary ensembles subject to an overall constraint that the eigenvalues lie in a hyperplane.

In this article we derive, using standard methods of Toeplitz theory, an asymptotic formula for certain large minors of Toeplitz matrices. Bump and Diaconis obtained the same asymptotics using representation theory, with an answer having a different form.

This paper connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a Riemnn-Hilbert problem and an associated system of integrable partial differential equations. In particular, we show that the Poissonization of the distribution function of this length can be identified as the Jimbo-Miwa-Ueno tau function. © 2001 Elsevier Science B.V. A...

Circulant matrix family occurs in various fields, applied in image processing, communications, signal processing, encoding and preconditioner. Meanwhile, the circulant matrices [1, 2] have been extended in many directions recently. The f(x)-circulant matrix is another natural extension of the research category, please refer to [3, 11]. Recently, some authors researched the circulant type matric...