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We consider the generalized Anderson model    Δ  +   ∑   n  ∈  Nω  n    P  n    , where   N   is a countable set,{   ω  n   }    n  ∈  Nare i.i.d. random variables and the    P  n    are rank    N  <  ∞    projections. For these models we prove theorem analogous to that of Jakšić–Last on the equivalence of the trace measureσ  n    (  ·  )   =  t  r   (   P  n    E   H  ω(  ·  )    P  n   )for    n  ∈  N    a.e. ω. Our model covers the dimer and polymer models.

Jakšić–Last theorem for higher rank perturbations