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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 41 open journal systems 


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

Mylène Maida, Université Paris-Sud


Abstract
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.


Full text: PDF

Pages: 1131-1150

Published on: August 25, 2007
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Electronic Journal of Probability. ISSN: 1083-6489