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A Fredholm determinant formula for Toeplitz determinants

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arxiv math/9907165 v1 pith:6SQZAYG4 submitted 1999-07-25 math.CA math.RT

Alexei Borodin , Andrei Okounkov This is my paper · ORCID
classification math.CAmath.RT
keywords determinanttoeplitzformulafredholmkernelactingadmitsauthors
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We prove a formula expressing a general n by n Toeplitz determinant as a Fredholm determinant of an operator 1-K acting on l_2({n,n+1,...}), where the kernel K admits an integral representation in terms of the symbol of the original Toeplitz matrix. The proof is based on the results of one of the authors, see math.RT/9907127, and a formula due to Gessel which expands any Toeplitz determinant into a series of Schur functions. We also consider 3 examples where the kernel involves the Gauss hypergeometric function and its degenerations.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    math.FA 2026-05 unverdicted novelty 7.0 of 10

    Proves Fredholm determinantal identity for tilted Toeplitz minors generalizing BOGC, with bialternant forms, Cauchy-Binet expansions, and asymptotic links to Airy kernel perturbations.

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