How to cite item

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

   
@article{ECP1655,
	author = {Göran Bergqvist and Peter Forrester},
	title = {Rank probabilities for real random $N\times N \times 2$ tensors},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {tensors; multi-way arrays; typical rank; random matrices},
	abstract = {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 gamma   and Barnes $G$-functions respectively. This is a rational number for $N$ odd   and a rational number multiplied by $\pi^{N/2}$ for $N$ even. The   probability to be of rank $N+1$ is $1-P_N$. The proof makes use of recent   results on the probability of having $k$ real generalized eigenvalues for   real random Gaussian $N\times N$ matrices. We also prove that $\log P_N=   (N^2/4)\log (e/4)+(\log N-1)/12-\zeta '(-1)+{\rm O}(1/N)$ for large $N$,   where $\zeta$ is the Riemann zeta function.},
	pages = {no. 55, 630-637},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1655},    
        url = {http://ecp.ejpecp.org/article/view/1655}}