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 (ββ,xcβ), where xcβ depends
on the deformation only and can be infinite.Comment: We thank Alice Guionnet and Ofer Zeitouni for explaining that one
assumption in an early version of this paper was superfluou