Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities
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Publication:640813
DOI10.4007/ANNALS.2011.174.2.12zbMATH Open1232.15006arXiv0905.0443OpenAlexW2963471558MaRDI QIDQ640813
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Publication date: 20 October 2011
Published in: (Search for Journal in Brave)
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 non-degenerate 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.
Full work available at URL: https://arxiv.org/abs/0905.0443
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