Local deformed semicircle law and complete delocalization for Wigner matrices with random potential
From MaRDI portal
Publication:5410905
DOI10.1063/1.4823718zbMath1288.82031arXiv1302.4532OpenAlexW2963349864MaRDI QIDQ5410905
Publication date: 17 April 2014
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1302.4532
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)
Related Items
Rank-uniform local law for Wigner matrices ⋮ Edge universality for deformed Wigner matrices ⋮ Extremal eigenvalues and eigenvectors of deformed Wigner matrices ⋮ Isotropic self-consistent equations for mean-field random matrices ⋮ Local law and Tracy-Widom limit for sparse random matrices ⋮ The phase transition in the ultrametric ensemble and local stability of Dyson Brownian motion ⋮ Mesoscopic perturbations of large random matrices ⋮ Convergence of local statistics of Dyson Brownian motion ⋮ Spectral statistics of sparse Erdős-Rényi graph Laplacians ⋮ Local law and rigidity for unitary Brownian motion ⋮ Gaussian fluctuations in the equipartition principle for Wigner matrices ⋮ Tracy-Widom law for the extreme eigenvalues of large signal-plus-noise matrices ⋮ Landscape complexity beyond invariance and the elastic manifold ⋮ Universality for random matrix flows with time-dependent density ⋮ On the support of the free additive convolution ⋮ Fixed energy universality of Dyson Brownian motion ⋮ On the mean-field equations for ferromagnetic spin systems ⋮ Non-ergodic delocalization in the Rosenzweig-Porter model ⋮ Extremal eigenvalues of sample covariance matrices with general population ⋮ Delocalization transition for critical Erdős-Rényi graphs ⋮ Rigidity and a mesoscopic central limit theorem for Dyson Brownian motion for general \(\beta\) and potentials ⋮ Local spectral statistics of the addition of random matrices ⋮ Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices ⋮ Bulk universality for deformed Wigner matrices ⋮ Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices ⋮ Gaussian fluctuations for linear spectral statistics of deformed Wigner matrices ⋮ Singular spectrum and recent results on hierarchical operators ⋮ Optimal multi-resolvent local laws for Wigner matrices ⋮ Spectral rigidity for addition of random matrices at the regular edge ⋮ 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
Cites Work
- Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
- The local semicircle law for a general class of random matrices
- Free convolution with a semicircular distribution and eigenvalues of spiked deformations of Wigner matrices
- Random matrices: universality of local eigenvalue statistics
- On universality of local edge regime for the deformed Gaussian unitary ensemble
- Universality of random matrices and local relaxation flow
- 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
- Local semicircle law and complete delocalization for Wigner random matrices
- Characteristic vectors of bordered matrices with infinite dimensions
- Regularization by free additive convolution, square and rectangular cases
- The analogues of entropy and of Fisher's information measure in free probability theory. I
- Processes with free increments
- Correlations for the circular Dyson Brownian motion model with Poisson initial conditions
- Bulk universality for generalized Wigner matrices
- Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
- From Gumbel to Tracy-Widom
- The local relaxation flow approach to universality of the local statistics for random matrices
- A new approach to subordination results in free probability
- Spectral measure of large random Hankel, Markov and Toeplitz matrices
- Free Random Variables
- Lectures on the Combinatorics of Free Probability
- An Introduction to Random Matrices
- A Brownian-Motion Model for the Eigenvalues of a Random Matrix
- On the free convolution with a semi-circular distribution
- Universality of local spectral statistics of random matrices
- Wegner Estimate and Level Repulsion for Wigner Random Matrices
- On the law of addition of random matrices.
- Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices
