2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225166We introduce a family of rotationally invariant random matrix ensembles characterized by a parameter $λ$. While $λ=1$ corresponds to well-known critical ensembles, we show that $λ\ne 1$ describes "Lévy like" ensembles, characterized by power law eigenvalue densities. For $λ> 1$ the density is bounded, as in Gaussian ensembles, but $λ<1$ describes ensembles characterized by densities with long tails. In particular, the model allows us to evaluate, in terms of a novel family of orthogonal polynomials, the eigenvalue correlations for Lévy like ensembles. These correlations differ qualitatively from those in either the Gaussian or the critical ensembles.9 pages, 5 figuresStatistical MechanicsMathematical Physicstext