Melonic dominance and the largest eigenvalue of a large random tensor

We consider a Gaussian rotationally invariant ensemble of random real totally symmetric tensors with independent normally distributed entries, and estimate the largest eigenvalue typical tensor in this by examining rate growth initial vector under successive applications nonlinear map defined tensor. In limit large number dimensions, we observe that simple form melonic dominance holds, quantity study is effectively determined single Feynman diagram arising from average over components. This computation suggests our dimensions proportional to square root as it for matrices.