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Rotationally invariant family of L\'evy like random matrix ensembles
We introduce a family of rotationally invariant random matrix ensembles
characterized by a parameter . While corresponds to
well-known critical ensembles, we show that describes "L\'evy
like" ensembles, characterized by power law eigenvalue densities. For the density is bounded, as in Gaussian ensembles, but
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 L\'evy like ensembles. These
correlations differ qualitatively from those in either the Gaussian or the
critical ensembles.Comment: 9 pages, 5 figure