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Linear statistics of random matrix ensembles at the spectrum edge associated with the Airy kernel
Min,Chao1; Chen,Yang2
2020
Source PublicationNuclear Physics B
ISSN0550-3213
Volume950
AbstractIn this paper, we study the large N behavior of the moment-generating function (MGF) of the linear statistics of N×N Hermitian matrices in the Gaussian unitary, symplectic, orthogonal ensembles (GUE, GSE, GOE) and Laguerre unitary, symplectic, orthogonal ensembles (LUE, LSE, LOE) at the edge of the spectrum. From the finite N Fredholm determinant expression of the MGF of the linear statistics [35], we find the large N asymptotics of the MGF associated with the Airy kernel in these Gaussian and Laguerre ensembles. Then we obtain the mean and variance of the suitably scaled linear statistics. We show that there is an equivalence between the large N behavior of the MGF of the scaled linear statistics in Gaussian and Laguerre ensembles, which leads to the statistical equivalence between the mean and variance of suitably scaled linear statistics in Gaussian and Laguerre ensembles. In the end, we use the Coulomb fluid method to obtain the mean and variance of another type of linear statistics in GUE, which reproduces the result of Basor and Widom [7].
DOI10.1016/j.nuclphysb.2019.114836
URLView the original
Language英语
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Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorChen,Yang
Affiliation1.School of Mathematical Sciences,Huaqiao University,Quanzhou,362021,China
2.Department of Mathematics,Faculty of Science and Technology,University of Macau,Macau,China
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Min,Chao,Chen,Yang. Linear statistics of random matrix ensembles at the spectrum edge associated with the Airy kernel[J]. Nuclear Physics B,2020,950.
APA Min,Chao,&Chen,Yang.(2020).Linear statistics of random matrix ensembles at the spectrum edge associated with the Airy kernel.Nuclear Physics B,950.
MLA Min,Chao,et al."Linear statistics of random matrix ensembles at the spectrum edge associated with the Airy kernel".Nuclear Physics B 950(2020).
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