Timeline for Correlations in last-passage percolation
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 28, 2011 at 12:02 | history | edited | James Martin | CC BY-SA 3.0 |
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| Dec 19, 2011 at 11:40 | comment | added | James Martin | btw, if the distribution of the weights has a sufficiently heavy tail (essentially, infinite variance) then the intersection will be $O(n)$: arxiv.org/abs/math/0604189 . I wonder if there could be some intermediate case? | |
| Dec 19, 2011 at 11:36 | comment | added | James Martin | Absolutely - the probability that the two semi-infinite geodesics do not intersect at all is a number that one could calculate exactly. My guess is that the covariance is indeed $O(1)$ but I don't know to show that. | |
| Dec 19, 2011 at 11:25 | history | edited | James Martin | CC BY-SA 3.0 |
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| Dec 19, 2011 at 10:21 | comment | added | Nathanael Berestycki | Hi James ! Thanks, very helpful. I guess the story about competing interface in FPP (which results in random slope) shows indeed that there is a nonzero probability that the geodesics have no edge in common at all. That is somehow slightly counterintuitive to me, you'd expect the geodesics to go get the same goodies for a while, before they diverge... So is the covariance $O(1)$ as well? | |
| Dec 19, 2011 at 10:13 | vote | accept | Nathanael Berestycki | ||
| Dec 19, 2011 at 4:21 | history | answered | James Martin | CC BY-SA 3.0 |