Displaying similar documents to “Spectral properties of large random matrices with independent entries”

Smallest singular value of sparse random matrices

Alexander E. Litvak, Omar Rivasplata (2012)

Studia Mathematica

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We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix and help to clarify the role of the variances...

Phase retrieval using random cubatures and fusion frames of positive semidefinite matrices

Martin Ehler, Manuel Gräf, Franz J. Király (2015)

Waves, Wavelets and Fractals

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As a generalization of the standard phase retrieval problem,we seek to reconstruct symmetric rank- 1 matrices from inner products with subclasses of positive semidefinite matrices. For such subclasses, we introduce random cubatures for spaces of multivariate polynomials based on moment conditions. The inner products with samples from sufficiently strong random cubatures allow the reconstruction of symmetric rank- 1 matrices with a decent probability by solving the feasibility problem...

Universality for certain hermitian Wigner matrices under weak moment conditions

Kurt Johansson (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We study the universality of the local eigenvalue statistics of Gaussian divisible Hermitian Wigner matrices. These random matrices are obtained by adding an independent GUE matrix to an Hermitian random matrix with independent elements, a Wigner matrix. We prove that Tracy–Widom universality holds at the edge in this class of random matrices under the optimal moment condition that there is a uniform bound on the fourth moment of the matrix elements. Furthermore, we show that universality...

Sparse recovery with pre-Gaussian random matrices

Simon Foucart, Ming-Jun Lai (2010)

Studia Mathematica

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For an m × N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by ℓ₁-minimization under the optimal condition m ≥ csln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes the ℓ₁-norm and the outer norm depends on probability distributions.

The random paving property for uniformly bounded matrices

Joel A. Tropp (2008)

Studia Mathematica

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This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original...