Displaying similar documents to “Concentration of the spectral measure of large Wishart matrices with dependent entries.”

Spectral properties of large random matrices with independent entries

P. Dueck, S. O'Rourke, D. Renfrew, A. Soshnikov (2011)

Banach Center Publications

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We consider large Wigner random matrices and related ensembles of real symmetric and Hermitian random matrices. Our results are related to the local spectral properties of these ensembles.

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...

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...