Fixed Energy Universality for Generalized Wigner Matrices

DOI10.1002/cpa.21624zbMath1354.15025arXiv1407.5606OpenAlexW2964063797MaRDI QIDQ2831147

László Erdős, Horng-Tzer Yau, Jun Yin, Paul Bourgade

Publication date: 2 November 2016

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.5606

zbMATH Keywords

random matricesspectrumuniversalityWigner matricesDyson Brownian motionmesoscopic statistics

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Brownian motion (60J65) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

Related Items (59)

CLT for non-Hermitian random band matrices with variance profiles ⋮ Fluctuations in the spectrum of non-Hermitian i.i.d. matrices ⋮ GOE statistics for Lévy matrices ⋮ Bulk universality for random lozenge tilings near straight boundaries and for tensor products ⋮ Normal fluctuation in quantum ergodicity for Wigner matrices ⋮ Extreme gaps between eigenvalues of Wigner matrices ⋮ The real Ginibre ensemble with \(k=O(n)\) real eigenvalues ⋮ Mesoscopic central limit theorem for general \(\beta\)-ensembles ⋮ Universality of the least singular value for sparse random matrices ⋮ Subcritical multiplicative chaos for regularized counting statistics from random matrix theory ⋮ Gaussian and non-Gaussian fluctuations for mesoscopic linear statistics in determinantal processes ⋮ Random matrices: overcrowding estimates for the spectrum ⋮ Convergence of local statistics of Dyson Brownian motion ⋮ Spectral statistics of sparse Erdős-Rényi graph Laplacians ⋮ Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős-Rényi graphs ⋮ Mesoscopic eigenvalue density correlations of Wigner matrices ⋮ Central Limit Theorem for Linear Eigenvalue Statistics of <scp>Non‐Hermitian</scp> Random Matrices ⋮ Local Kesten-McKay law for random regular graphs ⋮ Convergence rate to the Tracy-Widom laws for the largest eigenvalue of sample covariance matrices ⋮ Spectrum of random d‐regular graphs up to the edge ⋮ The least singular value of a random symmetric matrix ⋮ On the spectral form factor for random matrices ⋮ Combinatorics, probability and computing. Abstracts from the workshop held April 24--30, 2022 ⋮ Rigidity of eigenvalues for \(\beta\) ensemble in multi-cut regime ⋮ Quenched universality for deformed Wigner matrices ⋮ Single eigenvalue fluctuations of general Wigner-type matrices ⋮ Exponential growth of random determinants beyond invariance ⋮ Mesoscopic central limit theorem for non-Hermitian random matrices ⋮ Universality for random matrix flows with time-dependent density ⋮ Edge rigidity and universality of random regular graphs of intermediate degree ⋮ Large deviation principles via spherical integrals ⋮ Dyson Brownian motion for general \(\beta\) and potential at the edge ⋮ Comparison theorem for some extremal eigenvalue statistics ⋮ Bulk universality for generalized Wigner matrices with few moments ⋮ Applications of mesoscopic CLTs in random matrix theory ⋮ Local law of addition of random matrices on optimal scale ⋮ Mesoscopic fluctuations for unitary invariant ensembles ⋮ Universality in several-matrix models via approximate transport maps ⋮ Random matrices: tail bounds for gaps between eigenvalues ⋮ 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 ⋮ Gaussian fluctuations of the determinant of Wigner matrices ⋮ Cusp universality for random matrices. II: The real symmetric case ⋮ Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices ⋮ Universality of local statistics for noncolliding random walks ⋮ Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices ⋮ How much can the eigenvalues of a random Hermitian matrix fluctuate? ⋮ Eigenvector statistics of Lévy matrices ⋮ On fluctuations of global and mesoscopic linear statistics of generalized Wigner matrices ⋮ Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices ⋮ Mesoscopic central limit theorem for the circular \(\beta\)-ensembles and applications ⋮ Universality of the least singular value for the sum of random matrices ⋮ Fluctuation around the circular law for random matrices with real entries ⋮ Mesoscopic linear statistics of Wigner matrices of mixed symmetry class ⋮ Optimal delocalization for generalized Wigner matrices ⋮ Eigenvalues for the minors of Wigner matrices ⋮ Rigidity of the three-dimensional hierarchical Coulomb gas ⋮ High dimensional normality of noisy eigenvectors ⋮ Optimal local law and central limit theorem for \(\beta\)-ensembles

Cites Work

• Unnamed Item
• Unnamed Item
• The asymptotic distribution of a single eigenvalue gap of a Wigner matrix
• The local semicircle law for a general class of random matrices
• The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
• A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
• Edge universality of beta ensembles
• Gap universality of generalized Wigner and \(\beta\)-ensembles
• Random matrices: universality of local eigenvalue statistics
• Universality of random matrices and local relaxation flow
• Universality for generalized Wigner matrices with Bernoulli distribution
• Orthogonal and symplectic matrix models: universality and other properties
• Rigidity of eigenvalues of generalized Wigner matrices
• Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
• Local semicircle law and complete delocalization for Wigner random matrices
• Central limit theorem for linear eigenvalue statistics of the Wigner and the sample covariance random matrices
• Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
• Free hypercontractivity
• On orthogonal and symplectic matrix ensembles
• Bulk universality for generalized Wigner matrices
• On fluctuations of eigenvalues of random Hermitian matrices.
• Bulk universality for Wigner Hermite matrices with subexponential decay
• The local relaxation flow approach to universality of the local statistics for random matrices
• Universality of general \(\beta\)-ensembles
• Correlations between eigenvalues of a random matrix
• Bulk universality of general β-ensembles with non-convex potential
• Statistical Theory of the Energy Levels of Complex Systems. I
• On the density of Eigenvalues of a random matrix
• Bulk universality for Wigner matrices
• Universality of local spectral statistics of random matrices
• Wegner Estimate and Level Repulsion for Wigner Random Matrices
• Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices

This page was built for publication: Fixed Energy Universality for Generalized Wigner Matrices