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Hofmann-Credner, Katrin, Stolz, Michael (2008)
Electronic Communications in Probability [electronic only]
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Guionnet, Alice (2004)
Probability Surveys [electronic only]
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Soshnikov, Alexander (2004)
Electronic Communications in Probability [electronic only]
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Guntuboyina, Adityanand, Leeb, Hannes (2009)
Electronic Communications in Probability [electronic only]
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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.
L. Pastur (1996)
Annales de l'I.H.P. Physique théorique
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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...
Guionnet, A., Zeitouni, O. (2000)
Electronic Communications in Probability [electronic only]
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Iványi, Antal (2009)
Acta Universitatis Sapientiae. Mathematica
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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...
Chatterjee, Sourav, Ledoux, Michel (2009)
Electronic Communications in Probability [electronic only]
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Vladimirov, Igor, Thompson, Bevan (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Duheille-Bienvenüe, Frédérique, Guillotin-Plantard, Nadine (2003)
Electronic Communications in Probability [electronic only]
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Kargin, Vladislav (2009)
Electronic Communications in Probability [electronic only]
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