2009/03/20 by Jinmyung Choi, K. A. Muttalib · 4 citations
Mathematics · Physics and Astronomy · #Bounded function #Eigenvalues and eigenvectors #Gaussian #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Power law #Quantum chaos and dynamical systems #Quantum mechanics #Random Matrices and Applications #Random matrix #Statistical physics #Statistics #Stochastic processes and statistical mechanics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/42/15/152001
published in Journal of Physics A Mathematical and Theoretical 42(15), 152001 (Institute of Physics) · 9 pages, 5 figures
openalex publication_date 2009/03/20 · arxiv created 2009/03/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 '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.