Timeline for Consequence of equidistribution or not?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| S May 18 at 8:14 | history | suggested | The Amplitwist | CC BY-SA 4.0 |
fixed broken link to Wikipedia
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| May 18 at 5:42 | review | Suggested edits | |||
| S May 18 at 8:14 | |||||
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Oct 14, 2016 at 18:58 | comment | added | Charles | @GeorgeLowther Is there a standard reference for the case when we know the irrationality measure of θ? | |
| Oct 14, 2010 at 2:31 | comment | added | George Lowther | Well, my guess of $S_n=o(n^x)$ for every x > 1/2 and almost every $\theta$ was correct. We can't do much better than this, as Fedor's answer shows that $\limsup_{n\to\infty}|S_n|/n^x=\infty$ for every x < 1/2 and almost every $\theta$. | |
| Oct 14, 2010 at 1:42 | history | edited | George Lowther | CC BY-SA 2.5 |
answered follow-up question
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| Oct 13, 2010 at 20:52 | comment | added | George Lowther | ...although, trying a couple of plots with randomly chosen $\theta$, $S_n$ appears to be bounded, but is probably growing very slowly. | |
| Oct 13, 2010 at 20:20 | comment | added | George Lowther | I expect that $S_n=o(n^x)$ for every x > 1/2 and almost every $\theta$, by thinking of $S_n$ as similar to a random walk. I'll have to think about that a bit more though. | |
| Oct 13, 2010 at 18:40 | vote | accept | Portland | ||
| Oct 13, 2010 at 18:39 | comment | added | Portland | George, this is very nice. "There will be an uncountable dense set of irrational $\theta$ for which we can rule out bounds such as $S_n = O(n^x)$ with $x<1$." But is there any $\theta \in \mathbb{R}\setminus \mathbb{Q}$ s.t. there exists $x<1$ and $S_n = O(n^x)$, or can we rule that out as well? | |
| Oct 13, 2010 at 13:10 | history | edited | George Lowther | CC BY-SA 2.5 |
added 14 characters in body; edited body
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| Oct 13, 2010 at 13:04 | history | answered | George Lowther | CC BY-SA 2.5 |