We explore statistical correlations of collective nuclear excitations
under a multiparameter deformation of the Hamiltonian, in the framewor
k of the interacting boson model. The distribution of Hamiltonian matr
ix elements is found to behave as P(\H-ij\)proportional to 1/root\H-ij
\exp(-\H-ij\/V), with a parametric correlation of the type ln[H(x)H(y)
]proportional to-\x-y\. The studies are done in both the regular and c
haotic regimes of the Hamiltonian. Model-independent predictions for a
wide variety of correlation functions and distributions, which depend
on wave functions and energies, are made from parametric random matri
x theory and found to agree with the IBM results. Being a multiparamet
er theory, we consider general paths in parameter space and find that
universality can be effected by the topology of the parameter space. S
pecifically, Berry's phase can modify short distance correlations, bre
aking certain universal predictions.