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The celebrated Brascamp-Lieb (BL) inequalities (and their extensions) are an important mathematical tool, unifying and generalizing numerous inequalities in analysis, convex geometry and information theory.
Equilibrium points of bimatrix games
Carlton Lemke and J. T. Howson · 1964
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A relationship between arbitrary positive matrices and doubly stochastic matrices
R. Sinkhorn · 1964
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Maximum matching and a polyhedron with 0,1-vertices
Jack Edmonds · 1965
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Completely positive linear maps on complex matrices
Man-Duen Choi · 1975
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Best constants in Young’s inequality, its converse and its generalization to more than three functions
Herm Brascamp and Elliot Lieb · 1976
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Information geometry and alternating minimization procedures
Imre Csiszár and Gábor Tusnády · 1984
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Geometric Algorithms and Combinatorial Optimization
Martin Grötschel, László Lovász, and Alexander Schrijver · 1988
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Volumes of sections of cubes and related problems
Keith Ball · 1989
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Gaussian kernels have only Gaussian maximizers
Elliot Lieb · 1990
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On a reverse form of the Brascamp–Lieb inequality
Franck Barthe · 1998
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A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents
Nati Linial, Alex Samorodnitsky, and Avi Wigderson · 1998
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Semi-invariants of quivers and saturation for littlewood-richardson coefficients
Harm Derksen and Jerzy Weyman · 2000
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A deterministic polynomial-time algorithm for approximating mixed discriminant and mixed volume
Leonid Gurvits and Alex Samorodnitsky · 2000
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Semi-invariants of quivers as determinants
Mátyás Domokos and A. N. Zubkov · 2001
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Semi-invariants of quivers for arbitrary dimension vectors
Aidan Schofield and Michel Van den Bergh · 2001
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A linear lower bound on the unbounded error probabilistic communication complexity
Jürgen Forster · 2002
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Combinatorial Optimization: Polyhedra and Efficiency, Volume B
Alexander Schrijver · 2003
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Classical complexity and quantum entanglement
Leonid Gurvits · 2004
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Geometric complexity theory I: An approach to the P. vs. NP and related problems
Ketan Mulmuley and Milind Sohoni · 2006
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The combinatorics of quiver representations
Harm Derksen and Jerzy Weyman · 2007
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The Brascamp-Lieb inequalities: finiteness, structure, and extremals
Jonathan Bennett, Anthony Carbery, Michael Christ, and Terence Tao · 2008
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Finite bounds for Holder-Brascamp-Lieb multilinear inequalities
Jonathan Bennett, Anthony Carbery, Michael Christ, and Terence Tao · 2008
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Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities
Eric Carlen and Dario Cordero-Erausquin · 2009
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Some nonlinear Brascamp–Lieb inequalities and applications to harmonic analysis
Jonathan Bennett and Neal Bez · 2010
Understanding alternating minimization for matrix completion
Moritz Hardt · 2014
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Dictionary learning and tensor decomposition via the sum-of-squares method
Boaz Barak, Jonathan A Kelner, and David Steurer · 2015
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On Holder-Brascamp-Lieb inequalities for torsion-free discrete Abelian groups
Michael Christ, James Demmel, Nicholas Knight, Thomas Scanlon, and Katherine Yelick · 2015
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Polynomial degree bounds for matrix semi-invariants
Harm Derksen and Visu Makam · 2015
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Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors
Samuel B Hopkins, Tselil Schramm, Jonathan Shi, and David Steurer · 2015
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The Brascamp-Lieb polyhedron
Stefán Valdimarsson · 2010
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Geometric Brascamp-Lieb has the optimal best constant
Stefán Valdimarsson · 2011
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Stefanos Zafeiriou and Maria Petrou · 2011
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Fractional Sylvester-Gallai theorems
Boaz Barak, Zeev Dvir, Avi Wigderson, and Amir Yehudayoff · 2012
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Geometric Complexity Theory V: Equivalence between blackbox derandomization of polynomial identity testing and derandomization of Noether’s normalization lemma
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Communication lower bounds and optimal algorithms for programs that reference arrays - Part 1
Michael Christ, James Demmel, Nicholas Knight, Thomas Scanlon, and Katherine Yelick · 2013
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Gábor Ivanyos, Youming Qiao, and K. V. Subrahmanyam · 2015
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Mean value estimates for Weyl sums in two dimensions
Jean Bourgain and Ciprian Demeter · 2016
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Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three
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Rank bounds for design matrices with block entries and geometric applications
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A deterministic polynomial time algorithm for non-commutative rational identity testing
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Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation
Jingbo Liu, Thomas Courtarde, Paul Cuff, and Sergio Verdu · 2016
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Polynomial-time tensor decompositions with sum-of-squares
Tengyu Ma, Jonathan Shi, and David Steurer · 2016
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Maximizing determinants under partition constraints
Aleksandar Nikolov and Mohit Singh · 2016
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Behaviour of the Brascamp-Lieb constant
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Stability of the Brascamp-Lieb constant and applications
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Information-theoretic perspectives on Brascamp-Lieb inequality and its reverse
Jingbo Liu, Thomas Courtarde, Paul Cuff, and Sergio Verdu · 2017
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Sum of square proof for Brascamp-Lieb type inequality
Zhixian Lei and Yueqi Sheng · 2017
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