Timeline for GKS inequality with boundary condition
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2020 at 2:42 | comment | added | probsg | Yes, thanks a lot. I'll try it out. | |
| Sep 11, 2020 at 16:02 | comment | added | Yvan Velenik | @probsg I do not have an answer to your second, more specific question. If I had to solve it, then I'd try to use the high-temperature representation. It's a bit of a mess when you can have arbitrary boundary conditions, because of signs popping up, but they allow you to represent the expected value of $\sigma_x$ as a sum over paths from $x$ to $A$. This might allow you to exploit the fact that you have a tree structure (and thus only few available paths), which might lead to an inequality with an $o_n(1)$ term as you'd like. Not saying it would be trivial though. | |
| Sep 11, 2020 at 9:35 | comment | added | probsg | Yes, thank you. This is indeed helpful in the case that the external filed $h$ is large enough, say $h \geq -h_i$ for all $i$. | |
| Sep 11, 2020 at 8:58 | history | edited | Yvan Velenik | CC BY-SA 4.0 |
Added explanation
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| Sep 11, 2020 at 8:43 | comment | added | probsg | thank you so much Prof. Yvan Velenik for your answer. I have some further questions, please help me if you have suggestions. | |
| Sep 11, 2020 at 7:35 | history | edited | Yvan Velenik | CC BY-SA 4.0 |
added 10 characters in body
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| Sep 11, 2020 at 7:27 | history | answered | Yvan Velenik | CC BY-SA 4.0 |