Timeline for When is $\prod_{i=0}^\infty (I-x_i x_i^T)=0$ for isotropic Gaussian $x_i$?
Current License: CC BY-SA 4.0
10 events
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| Mar 23, 2023 at 20:42 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 23, 2023 at 20:41 | vote | accept | Yaroslav Bulatov | ||
| Mar 23, 2023 at 20:41 | comment | added | Yaroslav Bulatov | OK, everything makes sense now, thanks! | |
| Mar 23, 2023 at 20:39 | comment | added | Iosif Pinelis | @YaroslavBulatov : (i) Indeed, the necessity here is much harder to establish, because $\ln$ is easy to bound from above -- but not from below -- by tractable enough expressions. (ii) At the end of the answer, I have now provided details on $o(d^{-100})$. Please let me know if more details are needed. | |
| Mar 23, 2023 at 20:29 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 23, 2023 at 18:19 | comment | added | Yaroslav Bulatov | As I understand that you reduce matrix problem to figuring out if expected norm of a certain random vector is less than 0. Sufficient condition looks a lot easier to show than necessary! The one confusing part is where $O(d^{-100})$ comes from | |
| Mar 22, 2023 at 2:35 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 21, 2023 at 21:08 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 21, 2023 at 20:07 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 21, 2023 at 20:00 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |