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2007 Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles
Mylène Maida
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Electron. J. Probab. 12: 1131-1150 (2007). DOI: 10.1214/EJP.v12-438

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.

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Mylène Maida. "Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles." Electron. J. Probab. 12 1131 - 1150, 2007. https://doi.org/10.1214/EJP.v12-438

Information

Accepted: 25 August 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.60022
MathSciNet: MR2336602
Digital Object Identifier: 10.1214/EJP.v12-438

Subjects:
Primary: 60F10
Secondary: 15A52

Keywords: large deviations , random matrices

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