Spectral properties of the Jacobi ensembles via the Coulomb gas approach

Using the Coulomb gas method and standard methods of statistical physics, we compute analytically the joint cumulative probability distribution of the extreme eigenvalues of the Jacobi-MANOVA ensemble of random matrices in the limit of large matrices. This allows us to derive the rate functions for...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-11, Vol.45 (46), p.465005-26
Main Authors: Ramli, Huda Mohd, Katzav, Eytan, Castillo, Isaac Pérez
Format: Article
Language:English
Subjects:
canonical correlation analysis
Coulomb friction
Coulomb gas
Eigenvalues
Exact sciences and technology
Fluctuation
Jacobi ensemble
Mathematical analysis
Mathematical models
Matrices (mathematics)
Matrix methods
multivariate analysis of variance
Physics
random matrix theory
Spectra
Tracy-Widom distribution
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Summary:Using the Coulomb gas method and standard methods of statistical physics, we compute analytically the joint cumulative probability distribution of the extreme eigenvalues of the Jacobi-MANOVA ensemble of random matrices in the limit of large matrices. This allows us to derive the rate functions for the large fluctuations to the left and the right of the expected values of the smallest and largest eigenvalues analytically. Our findings are compared with some available known exact results as well as with numerical simulations finding good agreement.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/46/465005