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

被引：5
|
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
收藏
页码：153 / 160
页数：8
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