1111.0519 (Razvan Gurau)

Universality for Random Tensors    [PDF]

Razvan Gurau

We prove two universality results for random tensors of arbitrary rank D. We
first prove that, assuming that the tensor entries are N^D independent
identically distributed complex random variables then in the large N limit we
obtain a tensor distributed on a Gaussian. This generalizes the universality of
random matrices to random tensors.
We then prove a second, stronger, universality result. Under the weaker
assumption that the joint probability distribution of tensor entries is
invariant, we prove that in the large N limit we obtain again a tensor
distributed on a Gaussian. We emphasize that the covariance of the large N
Gaussian is not universal, but depends strongly on the details of the joint
distribution.

View original: http://arxiv.org/abs/1111.0519