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The smallest eigenvalue of large Hankel matrices generated by a deformed Laguerre weight
Mengkun Zhu1; Niall Emmart2; Yang Chen3; Charles Weems2
2019-01
Source PublicationMathematical Methods in the Applied Sciences
ISSN0170-4214
Volume42Issue:9Pages:3272-3288
Other Abstract

We study the asymptotic behavior of the smallest eigenvalue, lambda(N), of the Hankel (or moments) matrix denoted by HN=mu;m+n0 <= m,n <= N, with respect to the weight w(x)=x alpha e-x beta,x is an element of[0,infinity),alpha>-1,beta>12. An asymptotic expression of the polynomials orthogonal with w(x) is established. Using this, we obtain the specific asymptotic formulas of lambda(N) in this paper. Applying a parallel numerical algorithm, we get a variety of numerical results of lambda(N) corresponding to our theoretical calculations.

KeywordAsymptotics Hankel Matrices Random Matrix Smallest Eigenvalue Orthogonal Polynomials
DOIhttps://doi.org/10.1002/mma.5583
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000467275100021
PublisherWILEY, 111 RIVER ST, HOBOKEN 07030-5774, NJ USA
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorYang Chen
Affiliation1.School of Mathematics and Statistics,Qilu University of Technology (ShandongAcademy of Sciences), Jinan 250353,China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Avenida da Universidade, Macau,Taipa, China
3.College of Information and Computer Sciences, University of Massachusetts,Amherst, Massachusetts 01003
Recommended Citation
GB/T 7714
Mengkun Zhu,Niall Emmart,Yang Chen,et al. The smallest eigenvalue of large Hankel matrices generated by a deformed Laguerre weight[J]. Mathematical Methods in the Applied Sciences,2019,42(9):3272-3288.
APA Mengkun Zhu,Niall Emmart,Yang Chen,&Charles Weems.(2019).The smallest eigenvalue of large Hankel matrices generated by a deformed Laguerre weight.Mathematical Methods in the Applied Sciences,42(9),3272-3288.
MLA Mengkun Zhu,et al."The smallest eigenvalue of large Hankel matrices generated by a deformed Laguerre weight".Mathematical Methods in the Applied Sciences 42.9(2019):3272-3288.
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