Timeline for Is this graph of reciprocal power means always convex?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 21, 2014 at 21:57 | comment | added | Simon Willerton | If you take a large $N$, say $100$, and $n=N-1$ with $p=[1/N,1/N,\dots,1/N,2/N]$ then you get something that looks very non-convex. | |
| Jul 21, 2014 at 20:32 | comment | added | Dirk | Ok, my believe is destroyed… Another interesting question could be. What are $n$ and $p$ such that the respective function has most negative value in its second derivative? | |
| Jul 21, 2014 at 19:10 | history | edited | Tom Leinster | CC BY-SA 3.0 |
added 381 characters in body
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| Jul 21, 2014 at 19:05 | comment | added | Robert Israel | You can get a counterexample for arbitrary $n$ by perturbing this slightly ($p = [1/4, 1/4, 1/2 - (n-3) \epsilon, \epsilon, \ldots, \epsilon]$). | |
| Jul 21, 2014 at 19:05 | comment | added | Tom Leinster | Thanks very much, Dirk and Robert. I agree with Dirk: it's still a puzzle as to why it's so nearly true. E.g. in this particular example, the non-convexity is extremely subtle - I just plotted the graph and couldn't detect it by eye. | |
| Jul 21, 2014 at 19:03 | vote | accept | Tom Leinster | ||
| Jul 21, 2014 at 18:45 | comment | added | Dirk | Good! It still puzzles me, why the quantity is convex in almost every case. I would still believe if somebody told me that convexity is true for large $n$… | |
| Jul 21, 2014 at 17:45 | history | answered | Robert Israel | CC BY-SA 3.0 |