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The random banded matrices (RBM) whose diagonal elements fluctuate muchstronger than the off-diagonal ones were introduced recently by Shepelyansky asa convenient model for coherent propagation of two interacting particles in arandom potential. We treat the problem analytically by using the mapping ontothe same supersymmetric nonlinear $\sigma-$model that appeared earlier inconsideration of the standard RBM ensemble, but with renormalized parameters. ALorentzian form of the local density of states and a two-scale spatialstructure of the eigenfunctions revealed recently by Jacquod and Shepelyanskyare confirmed by direct calculation of the distribution of eigenfunctioncomponents.Comment: 7 pages,RevTex, no figures Submitted to Phys.Rev.

Statistical properties of random banded matrices with strongly fluctuating diagonal elements