Timeline for A "conjectured" concentration inequality for operators, probably related with random matrix theory
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 16, 2018 at 2:18 | history | edited | Morino_Hikari | CC BY-SA 3.0 |
added 89 characters in body
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| Apr 3, 2018 at 9:42 | vote | accept | Morino_Hikari | ||
| Apr 3, 2018 at 9:42 | |||||
| Apr 3, 2018 at 4:25 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 3.0 |
typo (I hope :) )
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| Apr 1, 2018 at 2:04 | comment | added | Morino_Hikari | Thank you for comments. That's true I am more concerned about the second inequality. I am trying to find out some uniform $\lambda$ that can bound such an operator inequality for any value of $\sigma$. And you are right even the estimation of the uniformly correct $\lambda$ should be based on the structure of the given partition (and about the distribution of X, I'm hoping quite slight constraints on it). The structure of $\Lambda(\sigma)$ is over-complicated and problem-specific and that is why I have not put it here. So is there any reference you could come up with as hints on tackling it? | |
| Mar 31, 2018 at 14:08 | comment | added | Jean Duchon | 1°) Your first identity needs the "cover" to be a "partition" of $\mathbb R^d$. 2°) As it is, the question has the trivial answer $\lambda=0$ (a sum of two positive semi-definite matrices, such as $XX^T$ and $YY^T$, is greater than each of them). 3°) You probably want something else, as maybe the conditional expectation of $XX^T$ given that $X\in\Lambda(\omega)$ is $\preceq\mathbb E[XX^T]+\lambda I$, don't you? That will depend on the partition and the distribution of $X$. | |
| Mar 31, 2018 at 7:40 | history | asked | Morino_Hikari | CC BY-SA 3.0 |