When Random Tensors meet Random Matrices. (arXiv:2112.12348v2 [math.PR] UPDATED)

Relying on random matrix theory (RMT), this paper studies asymmetric
order-$d$ spiked tensor models with Gaussian noise. Using the variational
definition of the singular vectors and values of (Lim, 2005), we show that the
analysis of the considered model boils down to the analysis of an equivalent
spiked symmetric block-wise random matrix, that is constructed from
contractions of the studied tensor with the singular vectors associated to its
best rank-1 approximation. Our approach allows the exact characterization of
the almost …

arxiv math pr random