Timeline for A natural fragmentation process
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2022 at 6:15 | comment | added | მამუკა ჯიბლაძე | @JamesPropp I confirm the statement in your comment. Seems like these oscillations are small compared to $n$. In fact, again experimenting, seems like $n\max_i|a_i-i/N|$ tends to 0 as $n$ increases. | |
| Feb 4, 2022 at 0:00 | comment | added | Kevin P. Costello | I believe some version of your question is addressed in Pyke's "The asymptotic behavior of spacings under Kakutani's model for interval subdivision" (Annals of Probability, 1980) | |
| Feb 3, 2022 at 22:37 | comment | added | James Propp | In my experiments, the maximum difference between $(a_1,...,a_n)$ and $(1/N,...,n/N)$ is small compared to $1/n$; I predict that the probability of there existing $i$ between 1 and $n$ such that $|a_i - i/N| > 1/n$ goes to zero as $n$ goes to infinity. I wonder if your code contains an error, or if mine does. | |
| Feb 3, 2022 at 21:53 | comment | added | მამუკა ჯიბლაძე | Could you make more precise the part about likely to be close to? Some experiments show that the list minus $(1/N,...n/N)$ might oscillate with increasing amplitude. | |
| Feb 3, 2022 at 21:40 | history | edited | James Propp | CC BY-SA 4.0 |
Made formula easier to read
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| Feb 2, 2022 at 21:43 | history | edited | James Propp | CC BY-SA 4.0 |
added 22 characters in body
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| Feb 2, 2022 at 21:03 | history | asked | James Propp | CC BY-SA 4.0 |