Gaussian random tensors of order D >= 3 admit multi-trace observables whose joint cumulants scale in N as strongly as the product of their one-trace expectations, so large N factorization fails in general.
LargeNlimit of irreducible tensor models:O(N) rank-3 tensors with mixed permutation symmetry,
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The large $N$ factorization does not hold for arbitrary multi-trace observables in random tensors
Gaussian random tensors of order D >= 3 admit multi-trace observables whose joint cumulants scale in N as strongly as the product of their one-trace expectations, so large N factorization fails in general.