The local semicircle law for a general class of random matrices
From MaRDI portal
Publication:388935
DOI10.1214/EJP.v18-2473zbMath1373.15053arXiv1212.0164OpenAlexW1979541448MaRDI QIDQ388935
László Erdős, Horng-Tzer Yau, Jun Yin, Antti Knowles
Publication date: 17 January 2014
Published in: Electronic Journal of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1212.0164
Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52)
Related Items (only showing first 100 items - show all)
Mesoscopic central limit theorem for non-Hermitian random matrices ⋮ Free energy fluctuations of the two-spin spherical SK model at critical temperature ⋮ GOE statistics for Lévy matrices ⋮ Rank-uniform local law for Wigner matrices ⋮ Local stability of the free additive convolution ⋮ Normal fluctuation in quantum ergodicity for Wigner matrices ⋮ Local semicircle law for Curie-Weiss type ensembles ⋮ Local spectral statistics of Gaussian matrices with correlated entries ⋮ The local semicircle law for random matrices with a fourfold symmetry ⋮ Edge universality for deformed Wigner matrices ⋮ Edge universality of correlated Gaussians ⋮ Universality of the least singular value for sparse random matrices ⋮ Extremal eigenvalues and eigenvectors of deformed Wigner matrices ⋮ On the principal components of sample covariance matrices ⋮ Hafnians, perfect matchings and Gaussian matrices ⋮ Bulk universality of sparse random matrices ⋮ Isotropic self-consistent equations for mean-field random matrices ⋮ Local law and Tracy-Widom limit for sparse random matrices ⋮ Local semicircle law under weak moment conditions ⋮ A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices ⋮ The phase transition in the ultrametric ensemble and local stability of Dyson Brownian motion ⋮ Random band matrices in the delocalized phase. III: Averaging fluctuations ⋮ Delocalization and diffusion profile for random band matrices ⋮ Convergence rate for spectral distribution of addition of random matrices ⋮ Convergence of local statistics of Dyson Brownian motion ⋮ Local law and Tracy-Widom limit for sparse stochastic block models ⋮ Spectral statistics of sparse Erdős-Rényi graph Laplacians ⋮ Averaging fluctuations in resolvents of random band matrices ⋮ Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős-Rényi graphs ⋮ Correlated random matrices: band rigidity and edge universality ⋮ Interval type local limit theorems for lattice type random variables and distributions ⋮ Mesoscopic eigenvalue density correlations of Wigner matrices ⋮ Universality for general Wigner-type matrices ⋮ Large deviation theorem for zeros of polynomials and Hermitian random matrices ⋮ Sample canonical correlation coefficients of high-dimensional random vectors: Local law and Tracy–Widom limit ⋮ Spectral graph matching and regularized quadratic relaxations. II: Erdős-Rényi graphs and universality ⋮ Central Limit Theorem for Linear Eigenvalue Statistics of <scp>Non‐Hermitian</scp> Random Matrices ⋮ Gaussian fluctuations in the equipartition principle for Wigner matrices ⋮ Bernoulli random matrices ⋮ Functional central limit theorems for Wigner matrices ⋮ Moment Inequalities for Linear and Nonlinear Statistics ⋮ Cusp universality for random matrices. I: Local law and the complex Hermitian case ⋮ Rare events in random matrix theory ⋮ On optimal bounds in the local semicircle law under four moment condition ⋮ Spectrum of random d‐regular graphs up to the edge ⋮ Edge statistics for Lozenge tilings of polygons. I: Concentration of height function on strip domains ⋮ The free field: realization via unbounded operators and Atiyah property ⋮ Level Statistics and Localization Transitions of Lévy Matrices ⋮ Eigenstate thermalisation hypothesis for translation invariant spin systems ⋮ On the rightmost eigenvalue of non-Hermitian random matrices ⋮ Quenched universality for deformed Wigner matrices ⋮ Non-backtracking spectra of weighted inhomogeneous random graphs ⋮ Comparison theorem for some extremal eigenvalue statistics ⋮ Stability of the matrix Dyson equation and random matrices with correlations ⋮ Bulk universality for generalized Wigner matrices with few moments ⋮ RANDOM MATRICES WITH SLOW CORRELATION DECAY ⋮ Global eigenvalue distribution of matrices defined by the skew-shift ⋮ A local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices ⋮ Local Semicircle Law under Moment Conditions: The Stieltjes Transform, Rigidity, and Delocalization ⋮ Extremal eigenvalues of sample covariance matrices with general population ⋮ Delocalization transition for critical Erdős-Rényi graphs ⋮ Eigenstate thermalization hypothesis for Wigner matrices ⋮ Anisotropic local laws for random matrices ⋮ Local deformed semicircle law and complete delocalization for Wigner matrices with random potential ⋮ Delocalization for a class of random block band matrices ⋮ The Altshuler-Shklovskii formulas for random band matrices. II: The general case ⋮ Local spectral statistics of the addition of random matrices ⋮ Diffusion profile for random band matrices: a short proof ⋮ Random characteristics for Wigner matrices ⋮ Edge universality of separable covariance matrices ⋮ Bounds on the norm of Wigner-type random matrices ⋮ Bulk universality for deformed Wigner matrices ⋮ A goodness-of-fit test for stochastic block models ⋮ The Altshuler-Shklovskii formulas for random band matrices. I: The unimodular case ⋮ Spiked separable covariance matrices and principal components ⋮ Inhomogeneous circular law for correlated matrices ⋮ On fluctuations of global and mesoscopic linear statistics of generalized Wigner matrices ⋮ Fluctuation around the circular law for random matrices with real entries ⋮ Spectral Properties of Wigner Matrices ⋮ Quadratic Vector Equations On Complex Upper Half-Plane ⋮ Bounds for the Stieltjes transform and the density of states of Wigner matrices ⋮ Local laws for polynomials of Wigner matrices ⋮ Scattering in quantum dots via noncommutative rational functions ⋮ Mesoscopic linear statistics of Wigner matrices of mixed symmetry class ⋮ Fixed Energy Universality for Generalized Wigner Matrices ⋮ Random band matrices in the delocalized phase. II: Generalized resolvent estimates ⋮ Singular spectrum and recent results on hierarchical operators ⋮ Location of the spectrum of Kronecker random matrices ⋮ Delocalization and continuous spectrum for ultrametric random operators ⋮ Equipartition principle for Wigner matrices ⋮ Thermalisation for Wigner matrices ⋮ Convergence and asymptotic approximations to universal distributions in probability ⋮ Optimal multi-resolvent local laws for Wigner matrices ⋮ Local semicircle law under fourth moment condition ⋮ Spectral rigidity for addition of random matrices at the regular edge ⋮ High dimensional normality of noisy eigenvectors ⋮ Delocalization and quantum diffusion of random band matrices in high dimensions. II: \(T\)-expansion ⋮ On Cramér-von Mises statistic for the spectral distribution of random matrices ⋮ Dyson Processes on the Octonion Algebra ⋮ Subordination for the sum of two random matrices
This page was built for publication: The local semicircle law for a general class of random matrices