Matrix Models for Beta Ensembles

Details Matrix Models for Beta Ensembles Matrix Models for Beta Ensembles

2002-06-25

arxiv.org/abs/math-ph/0206043v1

Physics

Mathematical Physics

LaTex, 22 pages

Scientific paper

10.1063/1.1507823

This paper constructs tridiagonal random matrix models for general ($\beta>0$) $\beta$-Hermite (Gaussian) and $\beta$-Laguerre (Wishart) ensembles. These generalize the well-known Gaussian and Wishart models for $\beta = 1,2,4$. Furthermore, in the cases of the $\beta$-Laguerre ensembles, we eliminate the exponent quantization present in the previously known models. We further discuss applications for the new matrix models, and present some open problems.

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