Reviews: Statistical mechanics of low-rank tensor decomposition

How is this connected with recent findings about the nice' landscape of the objective function associated with the decomposition of symmetric (orthogonal) order-4 tensors [1]? - The Gaussian assumption looks crucial for the analysis and seems to be guaranteed in the limit r N. Is this a typical situation in practice? Is always possible to compute the effective' variance for non-gaussian outputs? Is there a finite-N expansion that characterize the departure from Gaussianity in the non-ideal case? - For the themodynamic limit to hold, should one require N_alpha / N O(1) for all alpha?