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.
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AUTHOR = {Krasovsky, I. V.},
TITLE = {Correlations of the characteristic polynomials in the {G}aussian unitary ensemble or a singular {H}ankel determinant},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {139},
YEAR = {2007},
NUMBER = {3},
PAGES = {581--619},
ISSN = {0012-7094},
CODEN = {DUMJAO},
MRCLASS = {15A52 (41A60 47B35 82B44)},
MRNUMBER = {2350854},
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[KVA]
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TITLE = {The {R}iemann-{H}ilbert approach to strong asymptotics for orthogonal polynomials on {$[-1,1]$}},
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NUMBER = {2},
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[MMS1]
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[MMS2]
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}