Timeline for Examples where Kolmogorov's zero-one law gives probability 0 or 1 but hard to determine which?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Jul 31, 2010 at 16:30 | comment | added | Nate Eldredge | And in some cases, by "nontrivial" you mean "a well-known open problem." | |
| Oct 31, 2009 at 18:51 | vote | accept | Jason Dyer | ||
| Oct 27, 2009 at 22:53 | comment | added | David E Speyer | Adding or subtracting a finite number of edges can not change whether there is an infinite connected component. | |
| Oct 27, 2009 at 22:42 | comment | added | Ilya Nikokoshev | My question is: how do you know the Kolmogorov law applies in this case? | |
| Oct 27, 2009 at 22:34 | comment | added | David E Speyer | I don't follow. Here is a particular example: let G be the infinite square grid. Choose each edge to independently be present or absent with probability 1/2, thus obtain a random subgraph H. The 0-1 law tells us that the probability of H having an infinite connected component is either 0 or 1. Which? | |
| Oct 27, 2009 at 22:23 | comment | added | Ilya Nikokoshev |
This is not a clear-cut. I think there could also be values where p is between zero and one so I'm not sure the Kolmogorov theorem applies
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| Oct 27, 2009 at 22:13 | history | answered | Martin M. W. | CC BY-SA 2.5 |