Matrix models for beta ensembles

@article{Dumitriu2002MatrixMF,
  title={Matrix models for beta ensembles},
  author={Ioana Dumitriu and Alan Edelman},
  journal={Journal of Mathematical Physics},
  year={2002},
  volume={43},
  pages={5830-5847}
}
This paper constructs tridiagonal random matrix models for general (β>0) β-Hermite (Gaussian) and β-Laguerre (Wishart) ensembles. These generalize the well-known Gaussian and Wishart models for β=1,2,4. Furthermore, in the cases of the β-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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