Timeline for Which coupling of uniform random variables maximises the essential infimum of the sum?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 25 at 13:47 | comment | added | Ilya Bogdanov | Perhaps, it is just an easier version of partitioning $\{0,1,\dots,d\}$ into triples with the same sum (for a suitable $d$) which I was aquainted with before. I dont think I can add much more... | |
| Oct 25 at 13:33 | comment | added | Iosif Pinelis | "just found" :-) Pardon my insistence, but can you try to reconstruct the process of this finding? I want to learn more here. | |
| Oct 25 at 13:25 | comment | added | Ilya Bogdanov | No, I've just found a partition into triples of the form $(a,d/2+a,d-2a)$ and $(d/2+a,a,d-2a)$ ----s somehow, that was quick., | |
| Oct 25 at 13:17 | comment | added | Iosif Pinelis | @IlyaBogdanov : Did you use Mathematica or something like that for the discrete counterpart? I thought about first trying the discrete case this way, but then got distracted by other ideas, which are now seen as less fruitful. | |
| Oct 25 at 12:36 | comment | added | Ilya Bogdanov | @IosifPinelis i’ve just found a desired coupling when the variables are uniform on $\{0,1,\dots,d\}$; then it was easy to find a continuous analogue. | |
| Oct 25 at 12:05 | comment | added | Iosif Pinelis | Very nice! Can you disclose how you came up with this solution? | |
| Oct 25 at 11:56 | comment | added | Ilya Bogdanov | That’s why I wrote only this case, yes. | |
| Oct 25 at 11:42 | comment | added | Nate River | Nice and elementary! Concerning the general $n$ case, you can probably generalise this construction properly, but the essential infimum can also be obtained just by coupling together all remaining pairs into deterministic random variables that always sum to $1$, as mentioned by Iosif. | |
| Oct 25 at 11:38 | vote | accept | Nate River | ||
| Oct 25 at 11:29 | history | answered | Ilya Bogdanov | CC BY-SA 4.0 |