Eigenvalue distribution of random matrices : some recent results
L. Pastur (1996)
Annales de l'I.H.P. Physique théorique
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Displaying similar documents to “Poisson statistics for the largest eigenvalues of Wigner random matrices with heavy tails.”
Eigenvalue distribution of random matrices : some recent results
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Wigner theorems for random matrices with dependent entries: ensembles associated to symmetric spaces and sample covariance matrices.
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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.
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...
Eigenvalue distribution of random operators and matrices
Leonid Pastur (1991-1992)
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Yan V. Fyodorov, Hans-Jürgen Sommers, Boris A. Khoruzhenko (1998)
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Spectrum of random Toeplitz matrices with band structure.
Kargin, Vladislav (2009)
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An observation about submatrices.
Chatterjee, Sourav, Ledoux, Michel (2009)
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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...