  We analyze in full mathematical rigor the most general quartically perturbed
invariant probability measure for a random tensor. Using a version of the Loop
Vertex Expansion (which we call the mixed expansion) we show that the cumulants
write as explicit series in 1/N plus bounded rest terms. The mixed expansion
recasts the problem of determining the subleading corrections in 1/N into a
simple combinatorial problem of counting trees decorated by a finite number of
loop edges.
  As an aside, we use the mixed expansion to show that the (divergent)
perturbative expansion of the tensor models is Borel summable and to prove that
the cumulants respect an uniform scaling bound. In particular the quartically
perturbed measures fall, in the N to infinity limit, in the universality class
of Gaussian tensor models.
