THE SMALLEST EIGENVALUE OF LARGE HANKEL MATRICES ASSOCIATED WITH A SINGULARLY PERTURBED GAUSSIAN WEIGHT

被引：6

作者：

Wang, Dan ^{[1
]}

Zhu, Mengkun ^{[2
,3
]}

Chen, Yang ^{[3
]}

机构：

[1] Changzhou Univ, Sch Comp Sci & Artificial Intelligence, Dept Appl Math, Changzhou 213164, Peoples R China

[2] Qilu Univ Technol, Shandong Acad Sci, Sch Math & Stat, Jinan 250353, Peoples R China

[3] Univ Macau, Fac Sci & Technol, Dept Math, Ave Univ, Taipa, Macao, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 01期

关键词：

Hankel matrices; orthogonal polynomials; smallest eigenvalue; asymptotics;

D O I：

10.1090/proc/15757

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An asymptotic expression for the polynomials P-n(z), z is not an element of (-infinity, infinity), orthonormal with respect to a singularly perturbed Gaussian weight, exp(-z(2)- t/z(2)), z is an element of (-infinity, infinity), t > 0, is established. Based on this, the asymptotic behavior of the smallest eigenvalue of the Hankel matrix generated by the weight is described.

引用

页码：153 / 160

页数：8

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