One more proof of the Borodin-Okounkov formula for Toeplitz determinants

Borodin-Okounkov and Szegö for Toeplitz operators on model spaces

We consider the determinants of compressions of Toeplitz operators to finite-dimensional model spaces and establish analogues of the Borodin-Okounkov formula and the strong Szegö limit theorem in this setting.

On the determinant formulas by Borodin, Okounkov, Baik, Deift, and Rains

We give alternative proofs to (block case versions of) some formulas for Toeplitz and Fredholm determinants established recently by the authors of the title. Our proof of the Borodin-Okounkov formula is very short and direct. The proof of the Baik-Deift-Rains formulas is based on standard manipulations with Wiener-Hopf factorizations.

On a Toeplitz determinant identity of Borodin and Okounkov

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 combinatorial theory, in particular a theorem of Gessel expressing a Toeplitz determinant as a sum over partitions of products of Schur functions. The purpose of this note is to give two other proofs of the identity. The first uses an identity of the second author for the quotient of Toeplitz determinants in which the same product of Hankel matrices appears an…

倾斜Toeplitz子式的Borodin-Okounkov-Geronimo-Case恒等式

A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors

本文证明了倾斜Toeplitz子式的Fredholm行列式恒等式，将BOGC恒等式推广到Hardy空间的斜分割，并应用于周期TASEP中KPZ不动点的识别。

Determinant computations for some classes of Toeplitz-Hankel matrices

The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of the form $ (a_{i-j} \pm a_{i+j+1-k})_{i,j=0... N-1} $ with $k$ is fixed. We will show that this example as well as some general classes of operators have expansions that are similar to those that appear in the Strong Szegö Limit Theorem. We also obtain exact identitities for some of the determinants that are analogous to the one derived independently by Ger…

Szegö via Jacobi

At present there exist numerous different approaches to results on Toeplitz determinants of the type of Szegö's strong limit theorem. The intention of this paper is to show that Jacobi's theorem on the minors of the inverse matrix remains one of the most comfortable tools for tackling the matter. We repeat a known proof of the Borodin-Okounkov formula and thus of the strong Szegö limit theorem that is based on Jacobi's theorem. We then use Jacobi's theorem to derive exact and asymptotic formulas for Toeplitz determinants generated by functions with nonzero winding number. This derivation is ne…