Global spectrum fluctuations for the β-Hermite and β-Laguerre ensembles via matrix models
classification
🧮 math-ph
math.MP
keywords
betafluctuationsensemblesglobalhermitelaguerrematrixmodels
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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.
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