A matrix model for the \(\beta\)-Jacobi ensemble. (English) Zbl 1062.62509
Summary: This note presents a random matrix model for general (\(\beta>0\)) \(\beta\)-Jacobi ensembles. This generalizes the well-known MANOVA models for \(\beta = 1,2,4\) and eliminates the quantization of \(\beta\) (and other parameters) present in the previously known models. This model is a partial answer to an open problem presented by Dumitriu and Edelman, where they also presented models for the \(\beta\)-Laguerre and \(\beta\)-Hermite ensembles.
MSC:
| 62H99 | Multivariate analysis |
| 62J10 | Analysis of variance and covariance (ANOVA) |
| 15B52 | Random matrices (algebraic aspects) |
References:
| [1] | Dumitriu, J. Math. Phys. 43 pp 5830– (2002) |
| [2] | Dyson, J. Math. Phys. 3 pp 1199– (1963) |
| [3] | Forrester, P. J., ”Log-gases and random matrices,” pre-print http://www.ms.unimelb.edu.au/matpjf/matpjf.html (2002). · Zbl 0772.60098 |
| [4] | Forrester |
| [5] | Golub, G. H. and Van Loan, C. F.,Matrix Computations, 2nd ed. (Johns Hopkins University Press, Baltimore, MD, 1989). · Zbl 0733.65016 |
| [6] | Mehta, M. L.,Random Matrices, 2nd ed. (Academic, New York, 1991). |
| [7] | Muirhead, R. J.,Aspects of Multivariate Statistical Theory(Wiley, New York, 1982). · Zbl 0556.62028 |
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