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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)

—The breakdown point of signal subspace methods, which is the SNR below which the algorithm's performance deteriorates dramatically, is intimately related to the breakdown point of PCA based signal subspace estimation. We shed new light on this breakdown point for a broad class of signal-plus-noise models, provide a transparent derivation that highlights… (More)

- Florent Benaych-Georges, Sandrine Péché
- 2014

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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