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 full-rank general deformation. For the non-Gaussian ensembles, the deformation should be diagonal, and we assume that the laws of the entries have sharp sub-Gaussian 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:
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arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.13566
- arXiv:
- arXiv:1910.13566
- Bibcode:
- 2019arXiv191013566M
- Keywords:
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- Mathematics - Probability;
- 15B52;
- 60F10
- E-Print:
- We thank Alice Guionnet and Ofer Zeitouni for explaining that one assumption in an early version of this paper was superfluous