  We consider a random matrix model with both pairwise and non-pairwise
contracted indices. The partition function of the matrix model is similar to
that appearing in some replicated systems with random tensor couplings, such as
the p-spin spherical model for the spin glass. We analyze the model using
Feynman diagrammatic expansions, and provide an exhaustive characterization of
the graphs which dominate when the dimensions of the pairwise and (or)
non-pairwise contracted indices are large. We apply this to investigate the
properties of the wave function of a toy model closely related to a tensor
model in the Hamilton formalism, which is studied in a quantum gravity context,
and obtain a result in favor of the consistency of the quantum probabilistic
interpretation of this tensor model.
