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We study analytically the local density of states in a disorderednormal-metal wire at ballistic distance to a superconductor. Our calculation isbased on a scattering-matrix approach, which concerns for wave-functionlocalisation in the normal metal, and extends beyond the conventionalsemiclassical theory based on Usadel and Eilenberger equations. We also analysehow a finite transparency of the NS interface modifies the spectral proximityeffect and demonstrate that our results agree in the dirty diffusive limit withthose obtained from the Usadel equation.Comment: 12 pages, 8 figures, new section on Usadel equation is adde

Random matrix theory of the proximity effect in disordered wires