Global spectrum fluctuations for the β-Hermite and β-Laguerre ensembles via matrix models

We study the global spectrum fluctuations for β-Hermite and β-Laguerre ensembles via the tridiagonal matrix models introduced previously by the present authors [J. Math. Phys. 43, 5830 (2002)], and prove that the fluctuations describe a Gaussian process on polynomials. We extend our results to slightly larger classes of random matrices.