  In this paper we introduce an intermediate field representation for random
matrices and random tensors with positive (stable) interactions of degree
higher than 4. This representation respects the symmetry axis responsible for
positivity. It is non-perturbative and allows to prove that such models are
Borel-Le Roy summable of the appropriate order in their coupling constant.
However we have not been able yet to associate a convergent Loop Vertex
Expansion to this representation, hence our Borel summability result is not of
the optimal expected form when the size N of the matrix or of the tensor tends
to infinity.
