Disordered ensembles of random matrices

Abstract

It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable Lévy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. It is shown that the same procedure applied to random graphs gives rise to a family that interpolates between the Erdös-Renyi and the scale free models.

8 pages, 4 figures

References in corpus (16)

• Statistical mechanics of complex networks
• Level-Spacing Distributions and the Airy Kernel
• Superstatistics
• On Orthogonal and Symplectic Matrix Ensembles
• Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Periodic-Orbit Theory of Level Correlations
• Sparse random matrices: the eigenvalue spectrum revisited
• Gap probabilities in the finite and scaled Cauchy random matrix ensembles
• Random matrix ensembles from nonextensive entropy
• Family of generalized random matrix ensembles
• Spectral properties of empirical covariance matrices for data with power-law tails
• Non-extensive RMT Approach to Mixed Regular-Chaotic Dynamics
• Family of solvable generalized random-matrix ensembles with unitary symmetry
• Random matrix theory within superstatistics
• Fluctuations in the composite regime of a disordered growth model

Cited by in corpus (11)

• Joint probability densities of level spacing ratios in random matrices
• Deformations of the Tracy-Widom distribution
• Power-law deformation of Wishart-Laguerre ensembles of random matrices
• On scale-free and poly-scale behaviors of random hierarchical network
• Kappa-deformed random-matrix theory based on Kaniadakis statistics
• Decomposition of spectral density in individual eigenvalue contributions
• Typical kernel size and number of sparse random matrices over GF(q) - a statistical physics approach
• Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials
• 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
• Normal mode analysis of disordered random-matrix ensembles