Timeline for Wiener Sausages in Riemann Surfaces
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2011 at 19:45 | vote | accept | ght | ||
| Apr 4, 2011 at 19:45 | answer | added | ght | timeline score: 3 | |
| Apr 1, 2011 at 14:04 | history | edited | ght | CC BY-SA 2.5 |
added 87 characters in body
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| Mar 22, 2011 at 19:26 | comment | added | Jon Bannon | Welcome, Gabriel! | |
| Mar 22, 2011 at 18:34 | comment | added | ght | BTW, by just comparing with the Euclidean case you see that the behavior is quiet different in these two cases. | |
| Mar 22, 2011 at 18:32 | comment | added | ght | Thanks zhoraster. I'm familiar with these two papers but they focus on the case where $t$ is fixed and $r\to 0$. They essentially proved that in this scenario: $$ \mathbb{E}(\mathrm{vol}(W_{r}(t)))\sim \frac{\pi t}{\log(1/r)}+\frac{\pi t}{2\log(1/r)^2}(1+k-\log(2t)). $$ However, I'm interested in the case where $r$ is fixed and $t\to\infty$ as in the Euclidean case. | |
| Mar 22, 2011 at 15:29 | comment | added | zhoraster | Some further scholar googling gave a similar result: archive.numdam.org/ARCHIVE/CM/CM_1986__60_1/CM_1986__60_1_65_0/… for a dimension $\ge 3$. | |
| Mar 22, 2011 at 15:28 | comment | added | zhoraster | Quick scholar googling gave this reference: jstor.org/stable/2244253, which cites a similar result for general two-dimensional Riemann manifold (though the number 2 is missing from the rhs there). | |
| Mar 22, 2011 at 12:12 | history | asked | ght | CC BY-SA 2.5 |