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The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general random matrices in terms of an associated noncommutative model.
An introduction to the approximation of functions
T. J. Rivlin · 1969
Earlier work this paper cites.
Jensen’s inequality for positive contractions on operator algebras
D. Petz · 1987
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On the second eigenvalue of a graph
A. Nilli · 1991
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Matrix analysis
R. Bhatia · 1997
Earlier work this paper cites.
Free hypercontractivity
P. Biane · 1997
Earlier work this paper cites.
Computing norms of free operators with matrix coefficients
F. Lehner · 1999
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Operator Khintchine inequality in non-commutative probability
A. Buchholz · 2001
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An optimal L p L^{p} -bound on the Krein spectral shift function
D. Hundertmark and B. Simon · 2002
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Introduction to operator space theory
G. Pisier · 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
Earlier work this paper cites.
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
Earlier work this paper cites.
Eigenvalues of large sample covariance matrices of spiked population models
J. Baik and J. W. Silverstein · 2006
Earlier work this paper cites.
Lectures on the combinatorics of free probability
A. Nica and R. Speicher · 2006
Earlier work this paper cites.
Trace inequalities and quantum entropy: an introductory course
E. Carlen · 2010
Earlier work this paper cites.
Angular synchronization by eigenvectors and semidefinite programming
A. Singer · 2011
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Concentration inequalities
S. Boucheron, G. Lugosi, and P. Massart · 2013
Cited alongside, same era.
Decoding binary node labels from censored edge measurements: phase transition and efficient recovery
E. Abbe, A. S. Bandeira, A. Bracher, and A. Singer · 2014
Cited alongside, same era.
A statistical model for tensor PCA
A. Montanari and E. Richard · 2014
Cited alongside, same era.
Synchronization over Z 2 Z_{2} and community detection in signed multiplex networks with constraints
M. Cucuringu · 2015
Cited alongside, same era.
Tensor principal component analysis via sum-of-square proofs
S. B. Hopkins, J. Shi, and D. Steurer · 2015
Cited alongside, same era.
Spectral detection in the censored block model
A. Saade, M. Lelarge, F. Krzakala, and L. Zdeborová · 2015
Cited alongside, same era.
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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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
A. S. Bandeira, M. T. Boedihardjo, and R. van Handel · 2023
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Unpublished
A. S. Bandeira, G. Cipolloni, D. Schröder, and R. van Handel, March 2023 · 2023
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Norm of matrix-valued polynomials in random unitaries and permutations, 2023
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An introduction to matrix concentration inequalities
J. A. Tropp · 2015
Cited alongside, same era.
Optimality and sub-optimality of PCA for spiked random matrices and synchronization, 2016
A. Perry, A. S. Wein, A. S. Bandeira, and A. Moitra · 2016
Cited alongside, same era.
Spectrum of deformed random matrices and free probability
M. Capitaine and C. Donati-Martin · 2017
Cited alongside, same era.
Contextual stochastic block models
Y. Deshpande, S. Sen, A. Montanari, and E. Mossel · 2018
Cited alongside, same era.
Second-order matrix concentration inequalities
J. A. Tropp · 2018
Cited alongside, same era.
Largest eigenvalues of sparse inhomogeneous Erdős-Rényi graphs
F. Benaych-Georges, C. Bordenave, and A. Knowles · 2019
Cited alongside, same era.
C. Bordenave and B. Collins · 2023
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A simple and sharper proof of the hypergraph Moore bound
J.-T. Hsieh, P. K. Kothari, and S. Mohanty · 2023
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Optimal algorithms for the inhomogeneous spiked wigner model
A. Pak, J. Ko, and F. Krzakala · 2023
Later among the works it cites.
Universality and sharp matrix concentration inequalities
T. Brailovskaya and R. van Handel · 2024
Closest in time.
Exact bounds for some quadratic empirical processes with applications, 2024
Q. Han · 2024
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Phase transition for the generalized two-community stochastic block model
S. Lee and J. O. Lee · 2024
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Spectral phase transition and optimal PCA in block-structured spiked models
P. Mergny, J. Ko, and F. Krzakala · 2024
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Low-rank matrix estimation with inhomogeneous noise
A. Guionnet, J. Ko, F. Krzakala, and L. Zdeborová · 2025
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Computing extreme singular values of free operators, 2025
E. Parmaksiz and R. Van Handel · 2025
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