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

  title={Asymptotics of Toeplitz , Hankel , and Toeplitz + Hankel determinants with Fisher-Hartwig singularities},
  author={Percy Deift and Alexander Its and Igor Krasovsky},
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. 
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