A Note on Wiener-Hopf Determinants and the Borodin-Okounkov Identity

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。