Journal
ANNALS OF MATHEMATICS
Volume 174, Issue 2, Pages 1243-1299Publisher
Princeton Univ, Dept Mathematics
DOI: 10.4007/annals.2011.174.2.12
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Funding
- NSF [DMS-0500923, DMS-1001886, DMS-0701768]
- EPSRC [EP/F014198/1, EP/E022928/1]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1001886, 1001777] Funding Source: National Science Foundation
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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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