Timeline for Semistability of tensor products under automorphisms of tensored vector spaces
Current License: CC BY-SA 3.0
6 events
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| Aug 19, 2017 at 19:45 | comment | added | Will Sawin | @SMD No, being GIT-unstable still gives you a natural basis with an ordering, via the Hilbert-Mumford criterion, but there is no reason for the support to be an antichain in this basis. For instance, you could sum a stable tensor with an unstable tensor. | |
| Aug 19, 2017 at 19:23 | comment | added | SMD | Thank you @WillSawin! One more question: does being GIT-unstable for a tensor have anything to do with its support being an anti-chain? | |
| Aug 19, 2017 at 13:29 | comment | added | Will Sawin | @SMD (9) is the sharpest upper bound we have, and in particular is always at least as tight as theorem (4.10). So yes, there is a relationship, that the first bound is always at least as big as the second bound, which you should be able to prove directly by examining the proofs. (9) is often tight, and you can sometimes verify this using the techniques in that blog post. | |
| Aug 19, 2017 at 12:43 | comment | added | SMD | Hi @WillSawin. I have a question regarding the asymptotic slice rank of tensors: which upper bound - theorem (4.10) in arxiv.org/pdf/1605.06702.pdf or the inequality (9) in terrytao.wordpress.com/2016/08/24/… - is tight for a GIT-unstable tensor? or is there a relationship between the instability of a GIT-unstable tensor and the entropy of marginal distributions on its support? Thanks in advance! | |
| Jan 16, 2017 at 18:17 | history | edited | Will Sawin | CC BY-SA 3.0 |
added 2475 characters in body
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| Jan 15, 2017 at 22:36 | history | asked | Will Sawin | CC BY-SA 3.0 |