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Large N-limit for random matrices with external source with three distinct eigenvalues
Jian Xu1; Engui Fan2; Yang Chen3
2016-04-04
Source PublicationRandom Matrices: Theory and Applications
ISSN2010-3263
Volume5Issue:2Pages:1650005
Other Abstract

In this paper, we analyze the large N-limit for random matrix with external source with three distinct eigenvalues. And we confine ourselves in the Hermite case and the three distinct eigenvalues are −a,0,a−a,0,a. For the case a2>3a2>3, we establish the universal behavior of local eigenvalue correlations in the limit n→∞n→∞, which is known from unitarily invariant random matrix models. Thus, local eigenvalue correlations are expressed in terms of the sine kernel in the bulk and in terms of the Airy kernel at the edge of the spectrum. The result can be obtained by analyzing 4×44×4 Riemann–Hilbert problem via nonlinear steepest decent method.

KeywordRiemann–hilbert Problem Large N-limit Random Matrices Multiple Orthogonal Polynomi-als
DOIhttps://doi.org/10.1142/S2010326316500052
Language英語English
WOS Research AreaPhysics ; Mathematics
WOS SubjectPhysics, Mathematical ; Statistics & Probability
WOS IDWOS:000381054900002
PublisherWORLD SCI PUBL CO INC, 27 WARREN ST, STE 401-402, HACKENSACK, NJ 07601 USA
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorEngui Fan
Affiliation1.College of ScienceUniversity of Shanghai for Science and TechnologyShanghai 200093, P. R. China
2.School of Mathematical SciencesInstitute of Mathematics and Key Laboratoryof Mathematics for Nonlinear ScienceFudan University, Shanghai 200433, P. R. China
3.Department of MathematicsUniversity of Macau, Macau, P. R. China
Recommended Citation
GB/T 7714
Jian Xu,Engui Fan,Yang Chen. Large N-limit for random matrices with external source with three distinct eigenvalues[J]. Random Matrices: Theory and Applications,2016,5(2):1650005.
APA Jian Xu,Engui Fan,&Yang Chen.(2016).Large N-limit for random matrices with external source with three distinct eigenvalues.Random Matrices: Theory and Applications,5(2),1650005.
MLA Jian Xu,et al."Large N-limit for random matrices with external source with three distinct eigenvalues".Random Matrices: Theory and Applications 5.2(2016):1650005.
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