Spectral averaging techniques for Jacobi matrices
  Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the density of the averaged spectral measures. These Wegner type estimates are used to analyze stability properties for the spectral types of Jacobi matrices under local perturbations. 
Rafael del Rio, Carmen Martinez, Hermann Schulz-Baldes