Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities

Percy Deift, Alexander Its, Igor Krasovsky

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Abstract

We study the asymptotics in n for n-dimensional Toeplitz determinants whose symbols possess Fisher-Hartwig singularities on a smooth background. We prove the general nondegenerate asymptotic behavior as conjectured by Basor and Tracy. We also obtain asymptotics of Hankel determinants on a finite interval as well as determinants of Toeplitz+Hankel type. Our analysis is based on a study of the related system of orthogonal polynomials on the unit circle using the Riemann-Hilbert approach.

Original languageEnglish (US)
Pages (from-to)1243-1299
Number of pages57
JournalAnnals of Mathematics
Volume174
Issue number2
DOIs
StatePublished - Sep 1 2011

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ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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