Eigenvalue distribution of random operators and matrices
Leonid Pastur (1991-1992)
Séminaire Bourbaki
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Displaying similar documents to “Eigenvalue distribution of random matrices : some recent results”
Eigenvalue distribution of random operators and matrices
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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Universality in the random matrix spectra in the regime of weak non-hermiticity
Yan V. Fyodorov, Hans-Jürgen Sommers, Boris A. Khoruzhenko (1998)
Annales de l'I.H.P. Physique théorique
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Infinite products of random matrices and repeated interaction dynamics
Laurent Bruneau, Alain Joye, Marco Merkli (2010)
Annales de l'I.H.P. Probabilités et statistiques
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Let be a product of independent, identically distributed random matrices , with the properties that is bounded in , and that has a deterministic (constant) invariant vector. Assume that the probability of having only the simple eigenvalue 1 on the unit circle does not vanish. We show that is the sum of a fluctuating and a decaying process. The latter converges to zero almost surely, exponentially fast as →∞. The fluctuating part converges...
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.
The spectral laws of Hermitian block-matrices with large random blocks.
Oraby, Tamer F. (2007)
Electronic Communications in Probability [electronic only]
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The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
W. Hachem, P. Loubaton, J. Najim (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Central limit theorems for the products of random matrices sampled by a random walk.
Duheille-Bienvenüe, Frédérique, Guillotin-Plantard, Nadine (2003)
Electronic Communications in Probability [electronic only]
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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...