The outliers of a deformed Wigner matrix

Understand

We derive the joint asymptotic distribution of the outlier eigenvalues of an additively deformed Wigner matrix $H$.

• Our only assumptions on the deformation are that its rank be fixed and its norm bounded.
• Our results extend those of [The isotropic semicircle law and deformation of Wigner matrices.
• Preprint] by admitting overlapping outliers and by computing the joint distribution of all outliers.