A Fredholm determinant formula for Toeplitz determinants

Alexei Borodin, Andrei Okounkov

Research output: Contribution to journalArticlepeer-review

94 Citations (Scopus)


We prove a formula expressing a general n by n Toeplitz determinant as a Fredholm determinant of an operator 1 - K acting on l2(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 [14], 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.

Original languageEnglish
Pages (from-to)386-396
Number of pages11
JournalIntegral Equations and Operator Theory
Issue number4
Publication statusPublished - 2000
Externally publishedYes


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