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 , where depends on the deformation only and can be infinite.
The author would like to thank Paul Bourgade for many helpful discussions, and Alice Guionnet and Ofer Zeitouni for explaining that one assumption in an early version of this paper was superfluous.
"Large deviations for extreme eigenvalues of deformed Wigner random matrices." Electron. J. Probab. 26 1 - 37, 2021. https://doi.org/10.1214/20-EJP571