  Using the supersymmetry method we analytically calculate the local density of
states, the localiztion length, the generalized inverse participation ratios,
and the distribution function of eigenvector components for the superposition
of a random band matrix with a strongly fluctuating diagonal matrix. In this
way we extend previously known results for ordinary band matrices to the class
of random band matrices with preferential basis. Our analytical results are in
good agreement with (but more general than) recent numerical findings by
Jacquod and Shepelyansky.
