Extremal eigenvalues and eigenvectors of deformed Wigner matrices
From MaRDI portal
Publication:2634899
DOI10.1007/s00440-014-0610-8zbMath1338.15071OpenAlexW2020531132MaRDI QIDQ2634899
Publication date: 10 February 2016
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00440-014-0610-8
Stieltjes transformeigenvalueeigenvectorrandom matrixHermitian matrixlocalizationWigner matricesGaussian unitary ensembleTracy-Widom distributiondelocalizationlocal semicircle lawHelffer-Sjöstrand formula
Random matrices (probabilistic aspects) (60B20) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Limit theorems in probability theory (60F99)
Related Items
Linear low energy excitations in fully-connected models of glasses ⋮ Eigenvalues outside the bulk of inhomogeneous Erdős-Rényi random graphs ⋮ Local law and rigidity for unitary Brownian motion ⋮ Spiked multiplicative random matrices and principal components ⋮ Eigenvector delocalization for non‐Hermitian random matrices and applications ⋮ On the support of the free additive convolution ⋮ Extremal eigenvalues of sample covariance matrices with general population ⋮ Delocalization transition for critical Erdős-Rényi graphs ⋮ Bulk universality for deformed Wigner matrices ⋮ Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices ⋮ Eigenvectors and controllability of non-Hermitian random matrices and directed graphs ⋮ Gaussian fluctuations for linear spectral statistics of deformed Wigner matrices ⋮ Poisson statistics and localization at the spectral edge of sparse Erdős-Rényi graphs ⋮ Spherical Sherrington-Kirkpatrick model for deformed Wigner matrix with fast decaying edges ⋮ Bose–Einstein-like condensation of deformed random matrix: a replica approach
Cites Work
- Unnamed Item
- Unnamed Item
- Delocalization and diffusion profile for random band matrices
- Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
- Averaging fluctuations in resolvents of random band matrices
- The local semicircle law for a general class of random matrices
- Localization and delocalization of eigenvectors for heavy-tailed random matrices
- Free convolution with a semicircular distribution and eigenvalues of spiked deformations of Wigner matrices
- Quantum diffusion and eigenfunction delocalization in a random band matrix model
- On universality of local edge regime for the deformed Gaussian unitary ensemble
- Universality for generalized Wigner matrices with Bernoulli distribution
- Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation
- The arithmetic of distributions in free probability theory
- Rigidity of eigenvalues of generalized Wigner matrices
- Outliers in the spectrum of large deformed unitarily invariant models
- Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
- Bulk universality for deformed Wigner matrices
- Local semicircle law and complete delocalization for Wigner random matrices
- Poisson convergence for the largest eigenvalues of heavy tailed random matrices
- On the lower bound of the spectral norm of symmetric random matrices with independent entries
- Eigenvector localization for random band matrices with power law band width
- Regularization by free additive convolution, square and rectangular cases
- Absence of diffusion in the Anderson tight binding model for large disorder or low energy
- A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices
- Localization at large disorder and at extreme energies: an elementary derivation
- Level-spacing distributions and the Airy kernel
- Universality at the edge of the spectrum in Wigner random matrices.
- Poisson statistics for the largest eigenvalues of Wigner random matrices with heavy tails
- On orthogonal and symplectic matrix ensembles
- Bulk universality for generalized Wigner matrices
- Random matrices: Universality of local eigenvalue statistics up to the edge
- Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
- From Gumbel to Tracy-Widom
- A necessary and sufficient condition for edge universality of Wigner matrices
- Wigner random matrices with non-symmetrically distributed entries
- A new approach to subordination results in free probability
- Universality of Wigner random matrices: a survey of recent results
- Free Random Variables
- Linear Stability of a Plane Front in Solid Combustion at Large Heat of Reaction
- Universality of local eigenvalue statistics in random matrices with external source
- Lectures on the Combinatorics of Free Probability
- An Introduction to Random Matrices
- On the free convolution with a semi-circular distribution
- Wegner Estimate and Level Repulsion for Wigner Random Matrices
- Local deformed semicircle law and complete delocalization for Wigner matrices with random potential
- On the law of addition of random matrices.
