V.Baladi , L.-S.Young On the spectra of randomly perturbed expanding maps (145K, AmS TeX Version 2.1 (Postscript figure)) ABSTRACT. We consider small random perturbations of expanding and piecewise expanding maps and prove the robustness of their invariant densities and rates of mixing. We do this by proving the robustness of the spectra of their Perron-Frobenius operators.