Timeline for Collatz stopping-time and Poisson distribution, and connection to other problems?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 3 at 1:30 | comment | added | G Tony Jacobs | I understand from this answer that the distribution is a decent match for what one would expect, heuristically, from a stochastic process. However, I don't know much about the statistical properties of such processes. I see from the comments here that the variance is wrong for a Poisson distribution, so what kind of distribution is the good match, predicted by comparison with the stochastic process mentioned in this answer? Is it one of the well-known distributions? | |
| Apr 12, 2016 at 0:13 | comment | added | Gerald Edgar | So if you use all the $2$-adic integers, with its Haar measure, then it would have a nice distribution. But corresponding properties upon restricting to the rational integers (a set of probability zero) are not simple to prove, or even (so far) possible to prove. | |
| May 12, 2013 at 21:44 | comment | added | MarkusWave | Thank you for the answere. Indeed your explanation with the simple statistical model gives the same result for big n (and interesting deviations for smaller n - just tested it with mathematica). Very interesting that it follows the rules of random events for big numbers - did not expect. | |
| May 12, 2013 at 21:39 | vote | accept | MarkusWave | ||
| May 12, 2013 at 20:43 | history | answered | Stefan Kohl♦ | CC BY-SA 3.0 |