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Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization,”
 SIAM Review,
, 2010
"... Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and col ..."
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Cited by 562 (20 self)
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for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds
Shape fluctuations and random matrices
, 1999
"... We study a certain random growth model in two dimensions closely related to the onedimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the TracyWidom largest eigenvalue distribution for the Gaussian Uni ..."
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Cited by 398 (11 self)
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We study a certain random growth model in two dimensions closely related to the onedimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the TracyWidom largest eigenvalue distribution for the Gaussian
On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
 In STOC
, 2005
"... Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear co ..."
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Cited by 364 (6 self)
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Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear
Ranksparsity incoherence for matrix decomposition
, 2010
"... Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, and is intractable ..."
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Cited by 230 (21 self)
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and lowrank matrices playing a prominent role. When the sparse and lowrank matrices are drawn from certain natural random ensembles, we show that the sufficient conditions for exact recovery are satisfied with high probability. We conclude with simulation results on synthetic matrix decomposition
Seibergwitten theory and random partitions
"... We study N = 2 supersymmetric four dimensional gauge theories, in a certain N = 2 supergravity background, called Ωbackground. The partition function of the theory in the Ωbackground can be calculated explicitly. We investigate various representations for this partition function: a statistical sum ..."
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Cited by 267 (9 self)
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sum over random partitions, a partition function of the ensemble of random curves, a free fermion correlator. These representations allow to derive rigorously the SeibergWitten geometry, the curves, the differentials, and the prepotential. We study pure N = 2 theory, as well as the theory with matter
Discrete orthogonal polynomial ensembles and the Plancherel measure
, 2001
"... We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of as probability measures on partitions. The Meixner ensemble i ..."
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Cited by 189 (10 self)
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We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of as probability measures on partitions. The Meixner ensemble
ENSEMBLES
, 2001
"... Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain qgeneralizations of the Random Matrix Ensembles, which were first introduced in conne ..."
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Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain qgeneralizations of the Random Matrix Ensembles, which were first introduced
Universality of the Local Spacing Distribution in Certain Ensembles of Hermitian Wigner Matrices
 MATRICES, COMMUN. MATH. PHYS
, 2001
"... Consider an N × N hermitian random matrix with independent entries, not necessarily Gaussian, a so called Wigner matrix. It has been conjectured that the local spacing distribution, i.e. the distribution of the distance between nearest neighbour eigenvalues in some part of the spectrum is, in the ..."
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Cited by 102 (5 self)
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, in the limit as N → ∞, the same as that of hermitian random matrices from GUE. We prove this conjecture for a certain subclass of hermitian Wigner matrices.
Sparse and LowRank Matrix Decompositions
, 2009
"... Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, but obtaining an ex ..."
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Cited by 31 (2 self)
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by solving the semidefinite program. We also show that when the sparse and lowrank matrices are drawn from certain natural random ensembles, these sufficient conditions are satisfied with high probability. We conclude with simulation results on synthetic matrix decomposition problems.
Multiple orthogonal polynomial ensembles
, 2009
"... Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we introduce the notion of a multiple orthogonal polynomial ens ..."
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Cited by 27 (7 self)
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Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we introduce the notion of a multiple orthogonal polynomial
Results 1  10
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1,695