Florent Benaych-Georges

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AMS 2000 subject classifications: 15A52 46L54 60F99 Keywords: Random matrices Haar measure Free probability Phase transition Random eigenvalues Random eigenvectors Random perturbation Sample covariance matrices a b s t r a c t In this paper, we consider the singular values and singular vectors of finite, low rank perturbations of large rectangular random(More)
In this text, we consider an random N × N matrix X such that all but o(N) rows of X have W non identically zero entries, the other rows having less than W entries (such as, for example, standard or cyclic band matrices). We always suppose that 1 W N. We first prove that if the entries are independent, centered, have variance one, satisfy a certain tail(More)
These notes provide an introduction to the local semicircle law from random matrix theory, as well as some of its applications. We focus on Wigner matrices, Hermitian random matrices with independent upper-triangular entries with zero expectation and constant variance. We state and prove the local semicircle law, which says that the eigenvalue distribution(More)
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