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Global and Local Scaling Limits for the linear eigenvalues statitics of Jacobi beta-ensembles
Publication PlaceOperator Theory, Advances and Applications
PublisherSpringer Nature Switzerland AG 2022
Other Abstract

We study the moment-generating functions (MGF) for linear eigenvalue statistics of Jacobi unitary, symplectic and orthogonal ensembles. By expressing the MGF as Fredholm determinants of kernels of finite rank, we show that the mean and variance of the suitably scaled linear statistics in these Jacobi ensembles are related to the sine kernel in the bulk of the spectrum, whereas they are related to the Bessel kernel at the (hard) edge of the spectrum. The relation between the Jacobi symplectic/orthogonal ensemble (JSE/JOE) and the Jacobi unitary ensemble (JUE) is also established.

KeywordLinear Eigenvalue Statistics Jacobi Β-ensembles Moment-generating Function Mean And Variance Sine Kernel Bessel Kernel
MOST Discipline CatalogueMathematics
URLView the original
Indexed BySCIE
Document TypeJournal
CollectionFaculty of Science and Technology
Recommended Citation
GB/T 7714
CHEN YANG.Global and Local Scaling Limits for the linear eigenvalues statitics of Jacobi beta-ensembles[J].Operator Theory, Advances and Applications:Springer Nature Switzerland AG 2022,2022.
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