Timeline for Brownian motion of every point in the plane
Current License: CC BY-SA 3.0
17 events
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| Aug 13, 2014 at 18:35 | comment | added | Ori Gurel-Gurevich | Regarding the question in the edit: I interpreted it as asking for how many of the regions contain the origin. In that case, it tends to Poisson(1) regardless of the shapes. | |
| Aug 13, 2014 at 15:46 | vote | accept | JGH | ||
| Aug 13, 2014 at 15:03 | vote | accept | JGH | ||
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| Aug 13, 2014 at 15:03 | vote | accept | JGH | ||
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| Aug 13, 2014 at 15:00 | comment | added | j.c. | You might find this paper interesting, though it's about percolation properties of a disk packing in the plane, rather than what you've specifically asked about: arxiv.org/abs/1104.0762 | |
| Aug 13, 2014 at 14:16 | history | edited | JGH |
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| Aug 4, 2014 at 15:45 | vote | accept | JGH | ||
| Aug 13, 2014 at 14:16 | |||||
| Aug 4, 2014 at 15:40 | history | edited | JGH | CC BY-SA 3.0 |
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| Aug 4, 2014 at 15:38 | comment | added | JGH | @NateEldredge Independent motions. Are you saying the answer depends on the shapes of the regions? | |
| Aug 4, 2014 at 13:19 | comment | added | Nate Eldredge | As the answers point out, this question is incompletely posed, since you have not stated whether there is to be any dependence between these Brownian motions. (As pointed out by Robert Israel, if you want them all to be independent, you have measurability problems.) For the question in your edit, do you mean that each region should be translated according to an independent Brownian motion? I don't see how you can get a concrete answer without specifying the shapes of the regions. | |
| Aug 4, 2014 at 3:42 | comment | added | Douglas Zare | If the regions are anything like a square grid, then the distribution of the count approaches a Poisson distribution. | |
| Aug 4, 2014 at 3:41 | history | edited | JGH |
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| Aug 4, 2014 at 3:34 | history | edited | JGH | CC BY-SA 3.0 |
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| Aug 3, 2014 at 23:36 | answer | added | Robert Israel | timeline score: 5 | |
| Aug 3, 2014 at 22:55 | review | First posts | |||
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| Aug 3, 2014 at 22:53 | history | edited | JGH | CC BY-SA 3.0 |
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| Aug 3, 2014 at 22:47 | history | asked | JGH | CC BY-SA 3.0 |