  Low-lying collective states in nuclei are investigated in the framework of
the interacting boson model using an ensemble of random many-body interactions.
It is shown that whenever the number of bosons is sufficiently large compared
to the rank of the interactions, the spectral properties are characterized by a
dominance of L(P)=0(+) ground states and the occurrence of both vibrational and
rotational band structures. This indicates that these features represent a
general and robust property of the collective model space.
