Timeline for Entropy dominance of certain restricted sequenes
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 24, 2014 at 22:28 | comment | added | Turbo | added mathoverflow.net/questions/191438/… | |
| Dec 24, 2014 at 22:28 | vote | accept | Turbo | ||
| Dec 24, 2014 at 17:09 | comment | added | Turbo | The difficulty seems to be because if you add two variables that are close enough, the entropy may not noticeably change to be always strictly increasing. That is my intuition on these finite sequence artificial probability distribution. However I cannot rule out the fact that may be we can make the entropy strictly increasing by adding new variables somehow so that the variables $a_i$ do not converge to any limit. It would be interesting design sequences that diverge whose entropy is strictly increasing while the increase becomes smaller as $n$ increases. Thought that would be interesting. | |
| Dec 24, 2014 at 16:01 | comment | added | Bjørn Kjos-Hanssen | Sure you can formulate another one, maybe make sure to write something about what the difficulty seems to be | |
| Dec 24, 2014 at 11:35 | comment | added | Turbo | The following property also seems true. If $m+1\leq n$, then let $p$ correspond to $\{a_i\}_{i=1}^{m}$, $q$ correspond to $\{a_i\}_{i=1}^{m+1}$, $r$ correspond to $\{a_i\}_{i=1}^{n}$ and $s$ correspond to $\{a_i\}_{i=1}^{n+1}$ where $a_i$ satisfy properties above. Is it true that, $H(q)-H(p)>H(s)-H(r)$? Should I formulate another question. | |
| Dec 24, 2014 at 9:39 | history | edited | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |
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| Dec 24, 2014 at 9:26 | history | edited | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |
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| Dec 24, 2014 at 9:13 | history | edited | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |
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| Dec 24, 2014 at 9:03 | history | answered | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |