Timeline for Zeroes of the random Fibonacci sequence
Current License: CC BY-SA 3.0
15 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Sep 1, 2011 at 14:46 | vote | accept | JSE | ||
| Aug 31, 2011 at 21:07 | comment | added | j.c. | Thanks! The way to get the constant is still a bit mysterious to me, so if you have time, an update would be much appreciated. | |
| Aug 31, 2011 at 19:57 | comment | added | Gjergji Zaimi | I might update to clarify this, but I was mainly concerned with asymptotics and I forgot to mention that the upper bound is valid up to a constant factor. According to this answer here that constant is $\approx (3+\sqrt{5})/4$. mathoverflow.net/questions/63789/… | |
| Aug 31, 2011 at 19:34 | comment | added | j.c. | Hmmm, if one takes absolute values, the sequence must begin 0,1,1, then $X_3=$ either 2 or 0 with equal probability, but your upper bound is 3/8. Is it just an indexing issue? | |
| Aug 25, 2011 at 0:59 | comment | added | Gjergji Zaimi | @jc: the probability of $X_{3n}=0$ with absolute values is the same as the probability in the original sequence, it's a reflection principle. | |
| Aug 24, 2011 at 16:49 | comment | added | j.c. | This is quite nice but how do I transform these bounds to the non-absolute value sequence? It's probably some simple manipulation but I haven't had a chance to fully digest the paper yet. I'll update my plots if I can figure this out... | |
| Aug 22, 2011 at 4:24 | comment | added | Gerhard Paseman | The upper estimate can also be rewritten by replacing 3n choose n by 3((3n-1) choose (n-1)), which makes for a nicer comparison with the lower bound. Gerhard "Ask Me About System Design" Paseman, 2011.08.21 | |
| Aug 22, 2011 at 3:49 | history | edited | Gjergji Zaimi | CC BY-SA 3.0 |
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| Aug 22, 2011 at 0:17 | history | edited | Gjergji Zaimi | CC BY-SA 3.0 |
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| Aug 22, 2011 at 0:12 | history | edited | Gjergji Zaimi | CC BY-SA 3.0 |
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| Aug 21, 2011 at 23:51 | comment | added | Gjergji Zaimi | Ah, yes, I meant $X_{3n}$. | |
| Aug 21, 2011 at 23:44 | comment | added | j.c. | Do you mean the probability that $X_{3n}=0$ is bounded above by $(27/32)^n$? I observed a base of about $e^{-0.0764}\approx0.926$, and if I'm not miscalculating, your bound gives a base of $(27/32)^{1/3}\approx0.945$ which is rather close. | |
| Aug 21, 2011 at 23:32 | comment | added | j.c. | The paper link is here aero.tamu.edu/sites/default/files/faculty/kalmarnagy/… | |
| Aug 21, 2011 at 23:24 | history | answered | Gjergji Zaimi | CC BY-SA 3.0 |