Timeline for Entropy difference dominance of sequences
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2015 at 8:00 | comment | added | Turbo | Does the new questions have difficult answers? | |
| Dec 29, 2014 at 16:45 | comment | added | Bjørn Kjos-Hanssen | mathoverflow.net/questions/191678/…sequences | |
| Dec 29, 2014 at 2:43 | comment | added | Turbo | Addedhttp://mathoverflow.net/questions/191678/limiting-entropy-of-deterministic-sequences | |
| Dec 29, 2014 at 2:37 | vote | accept | Turbo | ||
| Dec 29, 2014 at 2:24 | comment | added | Bjørn Kjos-Hanssen | Another good question. .. maybe post it as such? | |
| Dec 29, 2014 at 2:18 | comment | added | Turbo | So for case $1$ entropy is infinite for all finite $k$? | |
| Dec 29, 2014 at 1:29 | comment | added | Bjørn Kjos-Hanssen | Yes if I understood you correctly | |
| Dec 26, 2014 at 19:52 | comment | added | Turbo | No it looks like for case $2$, $4,8,16,32,\dots$ case, the distribution approaches geometric with parameter $\frac{1}{2}$. Correct about this distribution assessment? | |
| Dec 26, 2014 at 19:42 | comment | added | Turbo | If we start with $a_1=4$. For $k=2$ in case $2$ we get $4,6,6+\log^2 6,6+2\log^2 6+\log^2(1+\frac{\log^2 6}{6}),\dots$ and it seems the distributions remain more or less 'close' to uniform and hence it looks like entropy should be $\infty$. For case $2$, we see the sequence $4,8,16,32,\dots$ and it looks like there will more weight to the probabilities associated with new $a_i$s. Entropy here too looks like it will go to $\infty$. Looks like I need to post another question. Shall I do that posts? | |
| Dec 26, 2014 at 19:26 | comment | added | Turbo | Thank you. I am looking for classifying distributions of the above type with finite and infinite entropy. I looked at en.wikipedia.org/wiki/Geometric_distribution and looked at the exact formula. It looks like geom distribution does not work. Anything else could help classify among the case 1 and 2? | |
| Dec 26, 2014 at 16:33 | comment | added | Bjørn Kjos-Hanssen | No, the entropy of the geometric distribution with parameter 1/2 is 2 not infinity | |
| Dec 26, 2014 at 9:29 | comment | added | Turbo | Actually can we still guess that $H(s)\rightarrow\infty$ always as $n\rightarrow\infty$? This is not very clear. | |
| Dec 25, 2014 at 21:38 | comment | added | Bjørn Kjos-Hanssen | Converges from below | |
| Dec 25, 2014 at 10:03 | history | edited | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |
added 74 characters in body
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| Dec 25, 2014 at 9:36 | history | answered | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |