Timeline for Quantum dynamics on varieties: asymptotic quantum trace distance on SHL varieties
Current License: CC BY-SA 3.0
6 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 22, 2012 at 17:14 | comment | added | Theo Johnson-Freyd | ... I will have to read the linked paper to understand why absolute-value-of-trace is the natural distance (I assume this is what you mean --- I don't know how to take the trace of "the absolute value of a matrix"), and not some other matrix norm that seems more natural to me (e.g. Hilbert-Schmidt norm). But probably for the maximum asymptotics you don't care, because there are probably AM-GM style inequalities. Anyway, once $\mathcal M_r^{(kk)}$ is made somehow compact or the norm is otherwise normalized, I like this question a lot. | |
| Feb 22, 2012 at 17:08 | comment | added | Theo Johnson-Freyd | A mathematical clarification question: You define the matrices in $\mathcal M_r^{(kk)}$ as "having unit trace norm", which is not a phrase I often come across --- I could imagine it meaning "unit trace", or "unit (matrix) norm", or.... But then you say that $\mathcal M_k^{(kk)}\cong\mathbb C^{k^2}$, so it seems that this condition is vacuous. In any case, am I right to think that the distance is asking "how far can a full-rank matrix be from any lower-rank matrix?"? If so, then you certainly do want some condition, or to normalize the distance somehow, else you get the answer $D_k=\infty$.... | |
| Feb 22, 2012 at 17:02 | comment | added | Theo Johnson-Freyd | Hi John, This looks like an improved version of mathoverflow.net/questions/88133, but I haven't read the question closely so I'm not sure if they are asking the same thing or are two questions on the same topic (certainly it's great to ask a series of related questions!). If the former, you can probably leave a link to this question at the top of the old one, and close the old one yourself; if you can't close it yourself, I'm sure you can leave a comment on meta asking it be closed. If the latter, then I hope you get good answers to both questions! | |
| Feb 11, 2012 at 19:12 | history | edited | John Sidles | CC BY-SA 3.0 |
Improved numeric estimate for D_8
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| Feb 11, 2012 at 18:13 | history | asked | John Sidles | CC BY-SA 3.0 |