Eigenvalue distribution for non-self-adjoint operators with small   multiplicative random perturbations
  In this work we continue the study of the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random perturbations, by treating the case of multiplicative perturbations in arbitrary dimension. We were led to quite essential improvements of many of the probabilistic aspects. 
Johannes Sjoestrand