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

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

2005-10-10

arxiv.org/abs/math-ph/0510043v2

Physics

Mathematical Physics

43 pages, 2 figures; typos corrected

Scientific paper

10.1063/1.2200144

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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