Rotationally invariant family of Lévy like random matrix ensembles

Abstract

We introduce a family of rotationally invariant random matrix ensembles characterized by a parameter $\lambda$. While $\lambda =1$ corresponds to well-known critical ensembles, we show that $\lambda \ne 1$ describes "Lévy like" ensembles, characterized by power law eigenvalue densities. For $\lambda >1$ the density is bounded, as in Gaussian ensembles, but $\lambda <1$ 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 figures

References in corpus (5)

• Scale free networks of earthquakes and aftershocks
• Probing NMSSM Scenarios with Minimal Fine-Tuning by Searching for Decays of the Upsilon to a Light CP-Odd Higgs Boson
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Information transfer through disordered media by diffuse waves
• Power law eigenvalue density, scaling and critical random matrix ensembles

Cited by in corpus (2)

• Local Tail Statistics of Heavy-Tailed Random Matrix Ensembles with Unitary Invariance
• Stable distributions and domains of attraction for unitarily invariant Hermitian random matrix ensembles