Global spectrum fluctuations for the ${\hat{I}}^2$-Hermite and ${\hat{I}}^2$-Laguerre ensembles via matrix models

Abstract

We study the global spectrum fluctuations for ${\hat{I}}^2$-Hermite and ${\hat{I}}^2$-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