Large deviations for extreme eigenvalues of deformed Wigner random matrices
Abstract
We present a large deviation principle at speed N for the largest eigenvalue of some additively deformed Wigner matrices. In particular this includes Gaussian ensembles with fullrank general deformation. For the nonGaussian ensembles, the deformation should be diagonal, and we assume that the laws of the entries have sharp subGaussian Laplace transforms and satisfy certain concentration properties. For these latter ensembles we establish the large deviation principle in a restricted range $(\infty, x_c)$, where $x_c$ depends on the deformation only and can be infinite.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 DOI:
 10.48550/arXiv.1910.13566
 arXiv:
 arXiv:1910.13566
 Bibcode:
 2019arXiv191013566M
 Keywords:

 Mathematics  Probability;
 15B52;
 60F10
 EPrint:
 We thank Alice Guionnet and Ofer Zeitouni for explaining that one assumption in an early version of this paper was superfluous