Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles
Probability
2019-08-06 v2
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 if 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 a previous work.
Cite
@article{arxiv.math/0609738,
title = {Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles},
author = {Mylène Maïda},
journal= {arXiv preprint arXiv:math/0609738},
year = {2019}
}
Comments
14 pages, new version with typos corrected in Theorem 3.2 and a new proof for Lemma 2.3. Many thanks to B. McKenna for pointing a mistake in the previous proof and proposing a more robust strategy through Lemma 2.5