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

• 成果类型: Article
• 署名作者: Deift, Percy; Its, Alexander; Krasovsky, Icor
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.174.2.12
• 发表日期: 2011
• 页码: 1243-1299
• 关键词: orthogonal polynomials; analytic weight; formulas; Respect; THEOREM; conjecture; matrices

摘要

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.