### Jinmyung Choi and K.A. Muttalib, *Rotationally invariant family of Levy-like random matrix ensembles*

**JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL**, 2009-03-20

Abstract: We 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 ̸= 1 describes ‘L´ evy-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 L´ evy-like ensembles. These correlations differ qualitatively from those in either the Gaussian or the critical ensembles.