Timeline for Probabilistic problem on random spanning trees
Current License: CC BY-SA 4.0
21 events
| when toggle format | what | by | license | comment | |
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| Jan 9 at 15:36 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
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| S Apr 27, 2023 at 19:05 | history | bounty ended | CommunityBot | ||
| S Apr 27, 2023 at 19:05 | history | notice removed | CommunityBot | ||
| Apr 26, 2023 at 2:07 | comment | added | fedja | @SophieMacDonald Yeah. The key words were actually those by Penelope: " I expect it can be false only when the both the first and the second factor (and therefore their product) are very close to $0$", so I just took a graph for which one expectation was exactly $0$ (a star with $4$ edges instead of two long loops), checked that the other one was negative, and then shifted the zero expectation up a tiny bit without altering the distributions too much. | |
| Apr 24, 2023 at 19:44 | comment | added | Sophie M | @fedja Beautiful! That's quite similar to what I was trying in my answer below, but the analysis of your graph is a lot simpler! | |
| Apr 20, 2023 at 1:43 | comment | added | fedja | I believe that the graph with root $v$ to which you attach 3 triangles with vertices (other than $v$) labeled $1$ and two very long loops with vertices labeled $-1$ is a counterexample. Check it! | |
| S Apr 19, 2023 at 17:14 | history | bounty started | Penelope Benenati | ||
| S Apr 19, 2023 at 17:14 | history | notice added | Penelope Benenati | Canonical answer required | |
| Apr 18, 2023 at 20:33 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
edited body
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| Apr 18, 2023 at 20:28 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
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| Apr 18, 2023 at 20:21 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
Added concentration inequalities hoping they can help
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| Apr 18, 2023 at 20:15 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
Added concentration inequalities hoping they can help
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| Apr 18, 2023 at 18:39 | answer | added | Sophie M | timeline score: 2 | |
| Apr 18, 2023 at 14:21 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
Raphrasing
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| Apr 18, 2023 at 10:14 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
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| Apr 18, 2023 at 10:11 | comment | added | Penelope Benenati | Thank you @SophieMacDonald for the question. I forgot to add $f$ to the question, as you can see reading now my post. I expect that the inequaility is true, and in the case I am wrong, I expect it can be false only when the both the first and the second factor (and therefore their product) are very close to $0$, say $o(g(\mathrm{degree}_G(v)))$ for some concave function $g\in C^{\infty}$ when $\mathrm{degree}_G(v)\to\infty$ in the counterexample class, which I expect to be infinite and containing arbitrarily large graphs. | |
| Apr 18, 2023 at 10:05 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
Added $f$ in the question with a universal quantifier
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| Apr 18, 2023 at 3:19 | comment | added | Sophie M | Also -- do you expect this to be true or false, i.e. do you expect a proof or a counterexample? Where did it come from? | |
| Apr 18, 2023 at 3:00 | comment | added | Sophie M | The function $f$ is fixed when taking the expectation? | |
| Apr 17, 2023 at 21:49 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
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| Apr 17, 2023 at 16:45 | history | asked | Penelope Benenati | CC BY-SA 4.0 |