Asymptotics of Toeplitz, Hankel, and Toeplitz plus Hankel determinants with Fisher-Hartwig singularities
Asymptotics of Toeplitz, Hankel, and Toeplitz plus Hankel determinants with Fisher-Hartwig singularities
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DOI：
10.4007/annals.2011.174.2.12
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发表时间：
2011-09-01
影响因子：
4.9
通讯作者：
Krasovsky, Icor
中科院分区：
文献类型：
--
作者：
Deift, Percy;Its, Alexander;Krasovsky, Icor
我们研究了符号在光滑背景下具有费希尔 - 哈特维格奇点的\(n\)维托普利兹行列式关于\(n\)的渐近性。我们证明了巴索尔和特雷西所猜想的一般非退化渐近行为。我们还得到了有限区间上汉克尔行列式以及托普利兹 + 汉克尔型行列式的渐近性。我们的分析是基于使用黎曼 - 希尔伯特方法对单位圆上相关正交多项式系的研究。
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.