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This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices.
A measure of the asymptotic efficiency for tests of a hypothesis based on the sum of observations
H. Chernoff · 1952
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Remarks on two theorems of E. Lieb
H. Epstein · 1973
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Convex trace functions and the Wigner–Yanase–Dyson conjecture
E. H. Lieb · 1973
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Expectations and entropy inequalities for finite quantum systems
G. Lindblad · 1974
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The moduli of smoothness and convexity and the Rademacher averages of trace classes S p S_{p} ( 1 ≤ p < ∞ ) (1\leq p<\infty)
N. Tomczak-Jaegermann · 1974
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D. A. Freedman · 1975
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Some inequalities for Gaussian processes and applications
Y. Gordon · 1985
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Matrix Analysis
R. A. Horn and C. R. Johnson · 1985
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Inégalités de Khintchine dans C p C_{p} ( 1 < p < ∞ ) (1<p<\infty)
F. Lust-Piquard · 1986
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The Symmetric Eigenvalue Problem
B. N. Parlett · 1987
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Noncommutative Khintchine and Paley inequalities
F. Lust-Piquard and G. Pisier · 1991
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Probability in Banach Spaces: Isoperimetry and Processes
M. Ledoux and M. Talagrand · 1991
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Majorization of Gaussian processes and geometric applications
Y. Gordon · 1992
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Topics in Matrix Analysis
R. A. Horn and C. R. Johnson · 1994
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A survey of certain trace inequalities
D. Petz · 1994
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Randomized Algorithms
R. Motwani and P. Raghavan · 1995
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Matrix Analysis
R. Bhatia · 1997
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Gaussian Measures
V. Bogdanov · 1998
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Large Deviations: Techniques and Applications
A. Dembo and O. Zeitouni · 1998
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Concentration
C. McDiarmid · 1998
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Random vectors in the isotropic position
M. Rudelson · 1999
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The expected norm of random matrices
Y. Seginer · 2000
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Operator Khintchine inequality in non-commutative probability
A. Buchholz · 2001
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Strong converse for identification via quantum channels
R. Ahlswede and A. Winter · 2002
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Decoupling: From Dependence to Independence
V. H. de la Peña and E. Giné · 2002
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Local operator theory, random matrices, and Banach spaces
K. R. Davidson and S. J. Szarek · 2002
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Completely Bounded Maps and Operator Algebras
Sampling from large matrices: An approach through geometric functional analysis
M. Rudelson and R. Vershynin · 2007
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Expansion properties of random Cayley graphs and vertex transitive graphs via matrix martingales
D. Cristofides and K. Markström · 2008
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Functions of Matrices: Theory and Computation
N. J. Higham · 2008
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Noncommutative Burkholder/Rosenthal inequalities II: Applications
M. Junge and Q. Xu · 2008
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On the conditioning of random subdictionaries
J. A. Tropp · 2008
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The fast Johnson–Lindenstrauss transform and approximate nearest neighbors
N. Ailon and B. Chazelle · 2009
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V. I. Paulsen · 2002
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Inequalities for quantum entropy: A review with conditions for equality
M. B. Ruskai · 2002
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Jensen’s operator inequality
F. Hansen and G. K. Pedersen · 2003
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Introduction to Operator Spaces
G. Pisier · 2003
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Optimal constants in Khintchine-type inequalities for Fermions, Rademachers and q q -Gaussian operators
A. Buchholz · 2005
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On the best constants in some non-commutative martingale inequalities
M. Junge and Q. Xu · 2005
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A matrix convexity approach to some celebrated quantum inequalities
E. G. Effros · 2009
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Concentration-of-measure inequalities
G. Lugosi · 2009
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Simpler approach to matrix completion
B. Recht · 2009
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Moment inequalities for sums of random matrices and their applications in optimization
A. M.-C. So · 2009
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A note on sums of independent random matrices after Ahlswede–Winter
R. Vershynin · 2009
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Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges
R. I. Oliveira · 2010
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Sums of random Hermitian matrices and an inequality by Rudelson
R. I. Oliveira · 2010
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Improved analysis of the subsampled randomized Hadamard transform
J. A. Tropp · 2010
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Recovering low-rank matrices from few coefficients in any basis
D. Gross · 2011
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Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions
N. Halko, P.-G. Martinsson, and J. A. Tropp · 2011
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Freedman’s inequality for matrix martingales
J. A. Tropp · 2011
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From the joint convexity of quantum relative entropy to a concavity theorem of Lieb
J. A. Tropp · 2011
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User-friendly tail bounds for matrix martingales
J. A. Tropp · 2011
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