  In this note we compare two recent results about the distribution of
eigenvalues for semi-classical pseudodifferential operators in two dimensions.
For classes of analytic operators A. Melin and the author obtained a complex
Bohr-Sommerfeld rule, showing that the eigenvalues are situated on a distorted
lattice. On the other hand, with M. Hager we showed in any dimension that Weyl
asymptotics holds with probability close to 1 for small random perturbations of
the operator. In both cases the eigenvalues distribute to leading order
according two smooth densities and we show here that the two densities are in
general different.
