Proves Fredholm determinantal identity for tilted Toeplitz minors generalizing BOGC, with bialternant forms, Cauchy-Binet expansions, and asymptotic links to Airy kernel perturbations.
Szeg\"o via Jacobi
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abstract
At present there exist numerous different approaches to results on Toeplitz determinants of the type of Szeg\"o'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 Szeg\"o 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 new and completely elementary
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2026 1verdicts
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A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors
Proves Fredholm determinantal identity for tilted Toeplitz minors generalizing BOGC, with bialternant forms, Cauchy-Binet expansions, and asymptotic links to Airy kernel perturbations.