Rank probabilities for real random $N\times N\times 2$ tensors

G. Bergqvist, P. J. Forrester

We prove that the probability $P_N$ for a real random Gaussian $N\times N\times 2$ tensor to be of real rank $N$ is $P_N=(\Gamma ((N+1)/2){)}^N/G(N+1)$, where $\Gamma (x)$, $G(x)$ denote the gam…