Poisson statistics for the largest eigenvalues of Wigner random matrices with heavy tails.
Soshnikov, Alexander (2004)
Electronic Communications in Probability [electronic only]
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Soshnikov, Alexander (2004)
Electronic Communications in Probability [electronic only]
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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.
Yan V. Fyodorov, Hans-Jürgen Sommers, Boris A. Khoruzhenko (1998)
Annales de l'I.H.P. Physique théorique
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Vladimirov, Igor, Thompson, Bevan (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Lee, Anna (1985-1986)
Portugaliae mathematica
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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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Tian, Yongge, Styan, George P.H. (2005)
Journal of Inequalities and Applications [electronic only]
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Kagan, Abram, Smith, Paul J. (1999)
Journal of Inequalities and Applications [electronic only]
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Hofmann-Credner, Katrin, Stolz, Michael (2008)
Electronic Communications in Probability [electronic only]
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Xiang Zhang, Qing-Wen Wang, Xin Liu (2012)
Open Mathematics
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Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively....
Zhang, Xian (2004)
Applied Mathematics E-Notes [electronic only]
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