Timeline for An Entropy Inequality (generalized)
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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| Aug 2, 2014 at 15:08 | answer | added | john mangual | timeline score: 1 | |
| Aug 2, 2013 at 17:01 | comment | added | Daniel Friedan | The main question is written in the language of the earlier question "An Entropy Inequality" (linked above). When $H_0$ and $H_1$ are commuting matrices, diagonalize them simultaneously. $H_0$ has eigenvalues $E_{0i}$ and $H_1$ has eigenvalues $E_{1i}$. The probability measures are $X(i)=e^{-E_{1i}}/Z(H_1)$ and $Y(i)=e^{-E_{0i}}/Z(H_0)$. $H_\alpha$ has eigenvalues $E_{\alpha i}=(1-\alpha) E_{0i}+\alpha E_{1i}$. $Z(i)= e^{-E_{\alpha i}}/Z(H_\alpha)$. Substituting, you'll see that the two versions of the inequality are the same. | |
| Aug 2, 2013 at 16:14 | comment | added | Suvrit | Does it hold even with the commuting assumption? Could you please write everything using matrices also in the main question (it makes it much easier to parse for people like me); thanks! | |
| Aug 2, 2013 at 15:45 | answer | added | Igor Rivin | timeline score: 1 | |
| Aug 2, 2013 at 14:43 | history | asked | Daniel Friedan | CC BY-SA 3.0 |