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Rank probabilities ...
Rank probabilities for real random NxNx2 tensors
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- Bergqvist, Göran (författare)
- Linköpings universitet,Tillämpad matematik,Tekniska högskolan
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- Forrester, Peter J. (författare)
- University of Melbourne, Victoria, Australia
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(creator_code:org_t)
- Institute of Mathematical Statistics / Bernoulli society. 2011
- 2011
- Engelska.
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Ingår i: Electronic Communications in Probability. - : Institute of Mathematical Statistics / Bernoulli society.. - 1083-589X. ; 16, s. 630-637
- Relaterad länk:
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https://liu.diva-por... (primary) (Raw object)
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- tensors
- multi-way arrays
- typical rank
- random matrices
- MATHEMATICS
- MATEMATIK
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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