Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles

By M. Maida. 2006

69 citations recorded by the source corpus.

We establish a large deviation principle for the largest eigenvalue of a rank one deformation of a matrix from the GUE or GOE. As a corollary, we get another proof of the phenomenon, well-known in learning theory and finance, that the largest eigenvalue separates from the bulk when the perturbation is large enough. A large part of the paper is devoted to an auxiliary result on the continuity of spherical integrals in the case when one of the matrix is of rank one, as studied in one of our previous works.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/75023dddc78937807215f9dd2ace59cb2e72eb85

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Citations in the corpus

On finite rank deformations of Wigner matrices (2011, background): “ Wigner matrices. Starting with the pioneering work by Fu¨redi and Koml´os [20], there have been several results on ﬁnite rank perturbations of matrices with i.i.d. entries, in particular [30], [19], [26], [12], [13], [14], [8], [9], [10], [35]. We also note several papers on the eigenvalues of samp”
Statistical thresholds for tensor PCA (2018, background): “For a small sample of work in this direction, see [43, 12, 15, 14].”
The Landscape of the Spiked Tensor Model (2017, methodology): “one deformation of the previous matrix. Instead of an exact representation, we use the asymptotic distribution of the eigenvalue of this matrix, as well as its large deviation properties, obtained in [Mai07]. 3 Related literature The complexity of random functions has been the object of large amount”
Large deviations of the extreme eigenvalues of random deformations of matrices (2010, unknown): “1 ha l-0 05 05 50 2, v er si on 2 - 31 A ug 2 01 0”
Large deviations for the largest eigenvalue of Rademacher matrices (2018, background): “1 from [22] (see [?] for an erratum) and Theorem 6.”
Outlier Eigenvalues for Deformed I.I.D. Random Matrices (2014, unknown): “Note that motivated by the seminal article of Baik, Ben Arous and Péché [6], previous works are devoted to the study of the outlier eigenvalues of deformed random Hermitian matrix models, see notably [4, 7, 8, 9, 10, 19, 21, 22, 23, 28, 34, 35, 36, 37, 41, 43, 45, 46].”
Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails (2015, background): “In [19], the author investigates the case of a GOE (respectively GUE) matrix perturbed by a rank one deterministic symmetric (respectively Hermitian) matrix.”