  We establish a large deviation principle for the largest eigenvalue of a rank
one deformation of a matrix from the GUE or GOE. As a corollary, we get another
proof of the phenomenon, well-known in learning theory and finance, that the
largest eigenvalue separates from the bulk if the perturbation is large enough.
A large part of the paper is devoted to an auxiliary result on the continuity
of spherical integrals, in the case when one of the matrix is of rank one, as
studied in a previous work.
