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We show that the dynamical order parameters can be reexpressed in terms ofthe distribution of the staggered auto-correlation and response functions. Wecalculate these distributions for the out of equilibrium dynamics of theSherrington-Kirpatrick model at long times. The results suggest that thelandscape this model visits at different long times in an out of equilibriumrelaxation process is, in a sense, self-similar. Furthermore, there is asimilarity between the landscape seen out of equilibrium at long times and theequilibrium landscape. The calculation is greatly simplified by making use ofthe superspace notation in the dynamical approach. This notation alsohighlights the rather mysterious formal connection between the dynamical andreplica approaches.Comment: 25 pages, Univ. di Roma I preprint #1049 (we replaced the file by the  RevTex file, figures available upon request

On the out-of-equilibrium order parameter in long-range spin-glasses