Global spectrum fluctuations for the $\beta$-Hermite and $\beta$-Laguerre ensembles via matrix models

Abstract

We study the global spectrum fluctuations for $\beta$-Hermite and $\beta$-Laguerre ensembles via the tridiagonal matrix models introduced in \cite{dumitriu02}, and prove that the fluctuations describe a Gaussian process on monomials. We extend our results to slightly larger classes of random matrices.

43 pages, 2 figures; typos corrected

References in corpus (4)

• Hermite and Laguerre $\beta$-ensembles: asymptotic corrections to the eigenvalue density
• Matrix models for circular ensembles
• MOPS: Multivariate Orthogonal Polynomials (symbolically)
• Orthogonal Polynomials and Fluctuations of Random Matrices

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