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Motivated by the Matrix Spencer conjecture, we study the problem of finding signed sums of matrices with a small matrix norm.
Rectangular confidence regions for the means of multivariate normal distributions
Zbyněk Šidák · 1967
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Roth’s estimate of the discrepancy of integer sequences is nearly sharp
József Beck · 1981
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“integer-making” theorems
József Beck and Tibor Fiala · 1981
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Problem complexity and method efficiency in optimization
Arkadi Semenovič Nemirovski and David Borisovich Yudin · 1983
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Six standard deviations suffice
Joel Spencer · 1985
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On the covering numbers of convex bodies
Hermann König and Vitali D Milman · 1987
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Extremal properties of orthogonal parallelepipeds and their applications to the geometry of banach spaces
Efim Davydovich Gluskin · 1989
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Non commutative khintchine and paley inequalities
Françoise Lust-Piquard and Gilles Pisier · 1991
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Sharp uniform convexity and smoothness inequalities for trace norms
Keith Ball, Eric A Carlen, and Elliott H Lieb · 1994
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Balancing vectors and gaussian measures of n-dimensional convex bodies
Wojciech Banaszczyk · 1998
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The discrepancy method: randomness and complexity
Bernard Chazelle · 2001
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Strong converse for identification via quantum channels
Rudolf Ahlswede and Andreas Winter · 2002
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Introduction to operator space theory
Gilles Pisier · 2003
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On the spectral norm of a random Toeplitz matrix
Mark Meckes · 2007
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Imre Bárány · 2008
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Geometric discrepancy: An illustrated guide
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Constructive algorithms for discrepancy minimization
Nikhil Bansal · 2010
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Iterative methods in combinatorial optimization
Lap Chi Lau, Ramamoorthi Ravi, and Mohit Singh · 2011
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A matrix hyperbolic cosine algorithm and applications
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The geometry of differential privacy: the sparse and approximate cases
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Towards a constructive version of banaszczyk’s vector balancing theorem
Daniel Dadush, Shashwat Garg, Shachar Lovett, and Aleksandar Nikolov · 2016
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Algorithmic discrepancy beyond partial coloring
Nikhil Bansal and Shashwat Garg · 2017
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Approximation-friendly discrepancy rounding
Nikhil Bansal and Viswanath Nagarajan · 2017
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Entropy numbers of embeddings of schatten classes
Aicke Hinrichs, Joscha Prochno, and Jan Vybiral · 2017
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Deterministic discrepancy minimization via the multiplicative weight update method
Avi Levy, Harishchandra Ramadas, and Thomas Rothvoss · 2017
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Constructive discrepancy minimization for convex sets
Thomas Rothvoss · 2017
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Better algorithms and hardness for broadcast scheduling via a discrepancy approach
Nikhil Bansal, Moses Charikar, Ravishankar Krishnaswamy, and Shi Li · 2014
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A simple proof of the gaussian correlation conjecture extended to multivariate gamma distributions
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Asymptotic geometric analysis, Part I
Shiri Artstein-Avidan, Apostolos Giannopoulos, and Vitali D Milman · 2015
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Convex optimization: Algorithms and complexity, 2015
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Constructive discrepancy minimization by walking on the edges
Shachar Lovett and Raghu Meka · 2015
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The gram-schmidt walk: a cure for the banaszczyk blues
Nikhil Bansal, Daniel Dadush, Shashwat Garg, and Shachar Lovett · 2018
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Balancing vectors in any norm
D. Dadush, A. Nikolov, K. Talwar, and N. Tomczak-Jaegermann · 2018
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Efficient algorithms for discrepancy minimization in convex sets
Ronen Eldan and Mohit Singh · 2018
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High-dimensional probability: An introduction with applications in data science
Roman Vershynin · 2018
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Four deviations suffice for rank 1 matrices
Rasmus Kyng, Kyle Luh, and Zhao Song · 2020
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Vector balancing in lebesgue spaces
Victor Reis and Thomas Rothvoss · 2020
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Matrix concentration inequalities and free probability
Afonso S Bandeira, March T Boedihardjo, and Ramon van Handel · 2021
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Matrix discrepancy from quantum communication
Samuel B Hopkins, Prasad Raghavendra, and Abhishek Shetty · 2021
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