liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Rank probabilities for real random NxNx2 tensors
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
University of Melbourne, Victoria, Australia.
2011 (English)In: Electronic Communications in Probability, ISSN 1083-589X, Vol. 16, 630-637 p.Article in journal (Refereed) Published
Abstract [en]

We prove that the probability P_N for a real random Gaussian NxNx2 tensor to be of real rank N is P_N=(Gamma((N+1)/2))^N/G(N+1), where Gamma(x) and G(x) denote the gamma and the 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 x N matrices. We also prove that log P_N= (N^2/4)log (e/4)+(log N-1)/12-zeta'(-1)+O(1/N) for large N, where zeta is the Riemann zeta function.

Place, publisher, year, edition, pages
Institute of Mathematical Statistics / Bernoulli society. , 2011. Vol. 16, 630-637 p.
Keyword [en]
tensors, multi-way arrays, typical rank, random matrices
National Category
URN: urn:nbn:se:liu:diva-72024DOI: 10.1214/ECP.v16-1655ISI: 000296162600001OAI: diva2:456014

Funding Agencies|Australian Research Council||

Available from: 2011-11-11 Created: 2011-11-11 Last updated: 2014-10-17

Open Access in DiVA

fulltext(203 kB)208 downloads
File information
File name FULLTEXT01.pdfFile size 203 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Bergqvist, Göran
By organisation
Applied MathematicsThe Institute of Technology
In the same journal
Electronic Communications in Probability

Search outside of DiVA

GoogleGoogle Scholar
Total: 208 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 158 hits
ReferencesLink to record
Permanent link

Direct link