Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach
arXiv:1208.2506 · doi:10.1088/1751-8113/45/46/465005
Abstract
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.
31 pages, 7 figures
References in corpus (7)
- Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
- Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
- Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy--Widom limits and rates of convergence
- Statistical distribution of quantum entanglement for a random bipartite state
- Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices
- Product of random projections, Jacobi ensembles and universality problems arising from free probability
- Approximate null distribution of the largest root in multivariate analysis