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.

We thank Alice Guionnet and Ofer Zeitouni for explaining that one assumption in an early version of this paper was superfluous

References in corpus (1)

• Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices

Cited by in corpus (2)

• Right large deviation principle for the top eigenvalue of the sum or product of invariant random matrices
• Stochastic and Quantum Dynamics of Repulsive Particles: from Random Matrix Theory to Trapped Fermions