Matrix models for beta ensembles

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. (C) 2002 American Institute of Physics.