On the localization transition in symmetric random matrices

Abstract

We study the behaviour of the inverse participation ratio and the localization transition in infinitely large random matrices through the cavity method. Results are shown for two ensembles of random matrices: Laplacian matrices on sparse random graphs and fully-connected Lévy matrices. We derive a critical line separating localized from extended states in the case of Lévy matrices. Comparison between theoretical results and diagonalization of finite random matrices is shown.

10 pages, 6 figures

References in corpus (20)

• Noise Dressing of Financial Correlation Matrices
• The Bethe lattice spin glass revisited
• Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
• Sparse random matrices: the eigenvalue spectrum revisited
• Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
• Spectra of Sparse Random Matrices
• Random incidence matrices: moments of the spectral density
• Rational Decisions, Random Matrices and Spin Glasses
• A single defect approximation for localized states on random lattices
• Cavity approach to the spectral density of non-Hermitian sparse matrices
• Anderson model on Bethe lattices: density of states, localization properties and isolated eigenvalue
• Localization, anomalous diffusion and slow relaxations: a random distance matrix approach
• Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids
• Random Levy Matrices Revisited
• Spectral properties of empirical covariance matrices for data with power-law tails
• Anderson Localization in Euclidean Random Matrices
• The phase diagram of Lévy spin glasses
• The Levy spin glass transition
• Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation
• Asymptotic behavior of the density of states on a random lattice

Cited by in corpus (54)

• The Lévy-Rosenzweig-Porter random matrix ensemble
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Spectral Theory of Sparse Non-Hermitian Random Matrices
• Level statistics and localization transitions of Lévy matrices
• Cavity and replica methods for the spectral density of sparse symmetric random matrices
• Finite size correction to the spectrum of regular random graphs: an analytical solution
• Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape
• Spectra of sparse non-Hermitian random matrices: an analytical solution
• Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
• Eigenvalue Outliers of non-Hermitian Random Matrices with a Local Tree Structure
• Large deviation function for the number of eigenvalues of sparse random graphs inside an interval
• Spectra of sparse regular graphs with loops
• Localization of eigenvectors in random graphs
• Spectra of Modular and Small-World Matrices
• Emergent percolation length and localization in random elastic networks
• The Spectral Backbone of Excitation Transport in Ultra-Cold Rydberg Gases
• Data-driven emergence of convolutional structure in neural networks
• First eigenvalue/eigenvector in sparse random symmetric matrices: influences of degree fluctuation
• Limitations in the spectral method for graph partitioning: detectability threshold and localization of eigenvectors
• Linear stability analysis for large dynamical systems on directed random graphs
• Localization and universality of eigenvectors in directed random graphs
• Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
• Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations
• A unifying model for random matrix theory in arbitrary space dimensions
• The spectral density of dense random networks and the breakdown of the Wigner semicircle law
• Analytic solution of the resolvent equations for heterogeneous random graphs: spectral and localization properties
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Lifshitz tails on the Bethe lattice: a combinatorial approach
• Extended Anderson Criticality in Heavy-Tailed Neural Networks
• Large deviation theory for diluted Wishart random matrices
• Top Eigenpair Statistics for Weighted Sparse Graphs
• Transition between localized and extended states in the hierarchical Anderson model
• Glassy dynamics on networks: local spectra and return probabilities
• Spectral properties of the trap model on sparse networks
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• Index statistical properties of sparse random graphs
• Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• From entropic to energetic barriers in glassy dynamics: The Barrat-Mézard trap model on sparse networks
• Moments of the inverse participation ratio for the Laplacian on finite regular graphs
• Localization in random bipartite graphs: numerical and empirical study
• Topological end states due to inhomogeneous strains in wrinkled semiconducting ribbons
• Effects of clustering heterogeneity on the spectral density of sparse networks
• Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
• Theory for the conditioned spectral density of non-invariant random matrices
• Fat-tailed distribution derived from first eigenvector of symmetric random sparse matrix
• Sparse Random Block Matrices
• Eigenvalue spectral tails and localization properties of asymmetric networks
• Epidemic threshold and localization of the SIS model on directed complex networks
• Phase transitions in atypical systems induced by a condensation transition on graphs
• Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization
• Top eigenpair statistics of diluted Wishart matrices
• Localization properties of the sparse Barrat-Mézard trap model
• "Spectrally gapped" random walks on networks: a Mean First Passage Time formula
• Statistical physics of principal minors: Cavity approach