High Dimensional Normality of Noisy Eigenvectors

[1]  A. Aggarwal,et al.  Eigenvector statistics of Lévy matrices , 2021 .

[2]  L. Benigni Fermionic eigenvector moment flow , 2019, Probability Theory and Related Fields.

[3]  Paul Bourgade,et al.  Extreme gaps between eigenvalues of Wigner matrices , 2018, Journal of the European Mathematical Society.

[4]  Fan Yang,et al.  Random band matrices in the delocalized phase, III: averaging fluctuations , 2020, Probability Theory and Related Fields.

[5]  A. Aggarwal,et al.  Eigenvector Statistics of L\'{e}vy Matrices , 2020, 2002.09355.

[6]  B. Landon,et al.  Comparison theorem for some extremal eigenvalue statistics , 2018, The Annals of Probability.

[7]  H. Yau,et al.  Random Band Matrices in the Delocalized Phase I: Quantum Unique Ergodicity and Universality , 2018, Communications on Pure and Applied Mathematics.

[8]  B. Landon,et al.  Spectral statistics of sparse Erdős–Rényi graph Laplacians , 2015, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.

[9]  Antti Knowles,et al.  Local law and complete eigenvector delocalization for supercritical Erdős–Rényi graphs , 2019, The Annals of Probability.

[10]  Ioana Dumitriu,et al.  Sparse general Wigner-type matrices: Local law and eigenvector delocalization , 2018, Journal of Mathematical Physics.

[11]  Random Band Matrices in the Delocalized Phase, II: Generalized Resolvent Estimates , 2018, Journal of Statistical Physics.

[12]  Paul Bourgade,et al.  The distribution of overlaps between eigenvectors of Ginibre matrices , 2018, Probability Theory and Related Fields.

[13]  Patrick Lopatto,et al.  Universality of the least singular value for sparse random matrices , 2017, Electronic Journal of Probability.

[14]  B. Landon,et al.  Local spectral statistics of the addition of random matrices , 2017, Probability Theory and Related Fields.

[15]  H. Yau,et al.  Fixed energy universality of Dyson Brownian motion , 2016, Advances in Mathematics.

[16]  Roman Vershynin,et al.  High-Dimensional Probability , 2018 .

[17]  Fan Yang,et al.  Random band matrices in the delocalized phase, III: averaging fluctuations , 2018, 1807.02447.

[18]  Amol Aggarwal,et al.  GOE statistics for Lévy matrices , 2018, Journal of the European Mathematical Society.

[19]  B. Eynard,et al.  Random matrices. , 2015, 1510.04430.

[20]  L. Benigni Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices , 2017, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.

[21]  H. Yau,et al.  A Dynamical Approach to Random Matrix Theory , 2017 .

[22]  Horng-Tzer Yau,et al.  Eigenvector Statistics of Sparse Random Matrices , 2016, 1609.09022.

[23]  H. Yau,et al.  Universality for a class of random band matrices , 2016, 1602.02312.

[24]  Van H. Vu,et al.  Eigenvectors of random matrices: A survey , 2016, J. Comb. Theory A.

[25]  B. Landon,et al.  Spectral statistics of sparse Erd\H{o}s-R\'enyi graph Laplacians , 2015 .

[26]  H. Yau,et al.  Bulk universality of sparse random matrices , 2015, 1504.05170.

[27]  H. Yau,et al.  Convergence of Local Statistics of Dyson Brownian Motion , 2015, 1504.03605.

[28]  Antti Knowles,et al.  Local Semicircle Law for Random Regular Graphs , 2015, 1503.08702.

[29]  H. Yau,et al.  Fixed Energy Universality for Generalized Wigner Matrices , 2014, 1407.5606.

[30]  H. Yau,et al.  The Eigenvector Moment Flow and Local Quantum Unique Ergodicity , 2013, 1312.1301.

[31]  A. Guionnet,et al.  Central limit theorem for eigenvectors of heavy tailed matrices , 2013, 1310.7435.

[32]  H. Yau,et al.  Isotropic local laws for sample covariance and generalized Wigner matrices , 2013, 1308.5729.

[33]  H. Yau,et al.  The local semicircle law for a general class of random matrices , 2012, 1212.0164.

[34]  H. Yau,et al.  Gap Universality of Generalized Wigner and beta-Ensembles , 2012, 1211.3786.

[35]  Oliver Pfaffel Wishart Processes , 2012, 1201.3256.

[36]  A. Guionnet,et al.  Localization and delocalization of eigenvectors for heavy-tailed random matrices , 2012, 1201.1862.

[37]  H. Yau,et al.  Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues , 2011, 1103.3869.

[38]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[39]  Terence Tao,et al.  Random matrices: Universal properties of eigenvectors , 2011, 1103.2801.

[40]  Jun Yin,et al.  Eigenvector distribution of Wigner matrices , 2011, 1102.0057.

[41]  H. Yau,et al.  Rigidity of eigenvalues of generalized Wigner matrices , 2010, 1007.4652.

[42]  H. Yau,et al.  Bulk universality for generalized Wigner matrices , 2010, 1001.3453.

[43]  T. Tao,et al.  Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge , 2009, 0908.1982.

[44]  Terence Tao,et al.  Smooth analysis of the condition number and the least singular value , 2008, Math. Comput..

[45]  Jun Yin,et al.  The local relaxation flow approach to universality of the local statistics for random matrices , 2009, 0911.3687.

[46]  H. Yau,et al.  Universality of random matrices and local relaxation flow , 2009, 0907.5605.

[47]  Terence Tao,et al.  Bulk universality for Wigner hermitian matrices with subexponential decay , 2009, 0906.4400.

[48]  T. Tao,et al.  Random matrices: Universality of local eigenvalue statistics , 2009, 0906.0510.

[49]  H. Yau,et al.  Wegner estimate and level repulsion for Wigner random matrices , 2008, 0811.2591.

[50]  T. Tao,et al.  Inverse Littlewood-Offord theorems and the condition number of random discrete matrices , 2005, math/0511215.

[51]  M. Stephanov,et al.  Random Matrices , 2005, hep-ph/0509286.

[52]  B. Collins Moments and cumulants of polynomial random variables on unitarygroups, the Itzykson-Zuber integral, and free probability , 2002, math-ph/0205010.

[53]  C. Landim,et al.  Relaxation to Equilibrium of Conservative Dynamics. I: Zero-Range Processes , 1999 .

[54]  P. Biane On the free convolution with a semi-circular distribution , 1997 .

[55]  Peter Sarnak,et al.  The behaviour of eigenstates of arithmetic hyperbolic manifolds , 1994 .

[56]  D. Stroock,et al.  Upper bounds for symmetric Markov transition functions , 1986 .

[57]  F. Dyson A Brownian‐Motion Model for the Eigenvalues of a Random Matrix , 1962 .

[58]  J. Nash Continuity of Solutions of Parabolic and Elliptic Equations , 1958 .

[59]  E. Wigner On the Distribution of the Roots of Certain Symmetric Matrices , 1958 .

[60]  E. Wigner Characteristic Vectors of Bordered Matrices with Infinite Dimensions I , 1955 .