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We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance.
Intermediate spaces and interpolation, the complex method
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The subgroup structure of the finite classical groups
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On the second eigenvalue of a graph
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Limit laws for random matrices and free products
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Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix
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Random Cayley graphs and expanders
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Spectral theory and differential operators
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Gaussian Hilbert spaces
S. Janson · 1997
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Finding a large hidden clique in a random graph
N. Alon, M. Krivelevich, and B. Sudakov · 1998
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M. Raab and A. Steger · 1998
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Computing norms of free operators with matrix coefficients
F. Lehner · 1999
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Random vectors in the isotropic position
M. Rudelson · 1999
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About the constants in Talagrand’s concentration inequalities for empirical processes
P. Massart · 2000
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Random graph coverings. I. General theory and graph connectivity
A. Amit and N. Linial · 2002
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Relative expanders or weakly relatively Ramanujan graphs
J. Friedman · 2003
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Introduction to operator space theory
G. Pisier · 2003
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Non-commutative L p L^{p} -spaces
G. Pisier and Q. Xu · 2003
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
J. Baik, G. Ben Arous, and S. Péché · 2005
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A new application of random matrices: Ext ( C red ∗ ( F 2 ) ) {\rm Ext}(C^{*}_{\rm red}(F_{2})) is not a group
U. Haagerup and S. Thorbjørnsen · 2005
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A generalization of the Lindeberg principle
S. Chatterjee · 2006
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Expander graphs and their applications
S. Hoory, N. Linial, and A. Wigderson · 2006
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Lectures on the combinatorics of free probability
A. Nica and R. Speicher · 2006
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Uniform expansion bounds for Cayley graphs of SL 2 ( 𝔽 p ) {\rm SL}_{2}(\mathbb{F}_{p})
J. Bourgain and A. Gamburd · 2008
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A proof of Alon’s second eigenvalue conjecture and related problems
J. Friedman · 2008
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Quasirandom groups
W. T. Gowers · 2008
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Random discrete matrices
V. Vu · 2008
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The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations
M. Capitaine, C. Donati-Martin, and D. Féral · 2009
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Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
A. Lytova and L. Pastur · 2009
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R. I. Oliveira · 2009
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An introduction to random matrices
G. W. Anderson, A. Guionnet, and O. Zeitouni · 2010
Free probability and random matrices
J. A. Mingo and R. Speicher · 2017
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Structured random matrices
R. van Handel · 2017
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On the convergence of the extremal eigenvalues of empirical covariance matrices with dependence
D. Chafaï and K. Tikhomirov · 2018
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Lower bounds for the smallest singular value of structured random matrices
N. Cook · 2018
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Size biased couplings and the spectral gap for random regular graphs
N. Cook, L. Goldstein, and T. Johnson · 2018
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The dimension-free structure of nonhomogeneous random matrices
R. Latała, R. van Handel, and P. Youssef · 2018
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Trace inequalities and quantum entropy: an introductory course
E. Carlen · 2010
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Complete isometries between subspaces of noncommutative L p L_{p} -spaces
M. de la Salle · 2010
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The spectral edge of some random band matrices
S. Sodin · 2010
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The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
F. Benaych-Georges and R. R. Nadakuditi · 2011
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Wiener chaos: moments, cumulants and diagrams
G. Peccati and M. S. Taqqu · 2011
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Spectral norm of products of random and deterministic matrices
R. Vershynin · 2011
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Second-order matrix concentration inequalities
J. A. Tropp · 2018
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Largest eigenvalues of sparse inhomogeneous Erdős-Rényi graphs
F. Benaych-Georges, C. Bordenave, and A. Knowles · 2019
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Eigenvalues of random lifts and polynomials of random permutation matrices
C. Bordenave and B. Collins · 2019
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Random matrices with slow correlation decay
L. Erdős, T. Krüger, and D. Schröder · 2019
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Quantum chaos on random Cayley graphs of SL 2 [ ℤ / p ℤ ] {\rm SL}_{2}[\mathbb{Z}/p\mathbb{Z}]
I. Rivin and N. T. Sardari · 2019
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The spectral norm of random lifts of matrices
A. S. Bandeira and Y. Ding · 2021
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Freeness over the diagonal and outliers detection in deformed random matrices with a variance profile
J. Bigot and C. Male · 2021
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A. S. Bandeira, D. Kunisky, D. G. Mixon, and X. Zeng · 2022
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On the non-asymptotic concentration of heteroskedastic Wishart-type matrix
T. T. Cai, R. Han, and A. R. Zhang · 2022
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Phase transition in the generalized stochastic block model, 2022
S. M. Lee and J. O. Lee · 2022
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Non-backtracking spectra of weighted inhomogeneous random graphs
L. Stephan and L. Massoulié · 2022
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BBP phenomena for deformed random band matrices, 2023
B. Au · 2023
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Matrix concentration inequalities and free probability
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Norm of matrix-valued polynomials in random unitaries and permutations, 2023
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On pseudospectrum of inhomogeneous non-Hermitian random matrices, 2023
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Matrix concentration inequalities with dependent summands and sharp leading-order terms, 2023
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Matrix concentration inequalities and free probability II. Two-sided bounds and applications, 2024
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A new approach to strong convergence, 2024
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Extreme singular values of inhomogeneous sparse random rectangular matrices
I. Dumitriu and Y. Zhu · 2024
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N. Zhivotovskiy · 2024
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