  A recently proposed statistical theory of the mean fields associated with the
ground and excited collective states of a generic many-body system is extended
by increasing the dimensions of the P-space. In applying the new framework to
nuclear matter, in addition to the mean field energies we obtain their
fluctuations as well, together with the ones of the wavefunctions, in first
order of the expansion in the complexity of the Q-space states. The physics
described by the latter is assumed to be random. To extract numerical
predictions out of our scheme we develop a schematic version of the approach,
which, while much simplified, yields results of significance on the size of the
error affecting the mean fields, on the magnitude of the residual effective
interaction, on the ground state spectroscopic factor and on the mixing
occurring between the vectors spanning the P-space.
