Timeline for Random walk on a simple finite network
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 21, 2011 at 20:45 | vote | accept | Michał Oszmaniec | ||
| Feb 19, 2011 at 22:55 | answer | added | Omer | timeline score: 12 | |
| Feb 19, 2011 at 22:36 | comment | added | Anthony Quas | It's probably helpful to define $X$ and $Y$ (especially they're not the same as $x$ and $y$): $Y=x+y$. I would call this the level of the point. The top level is level 0 and the bottom level in $N-1$. $X$ is then given by $X=x-(x+y)/2$. The $X$ coordinate in level $i$ goes from $-i/2$ to $i/2$. | |
| Feb 19, 2011 at 20:44 | comment | added | fedja | It does follow if you can show that the boundary values are concave on each side. Unfortunately, I failed to show that so far. I'll think of it more in the evening. | |
| Feb 19, 2011 at 20:16 | comment | added | George Lowther | That argument sounds rather tricky, but I think it is clear that letting $\mathbb{P}(X,Y)$ be the probability of hitting 0 from point (X,Y) then, for given Y, this is symmetric in X. That is is increasing for $X\le0$ should follow from the iterative definition of $\mathbb{P}(\cdot)$. | |
| Feb 19, 2011 at 18:24 | history | edited | Michał Oszmaniec | CC BY-SA 2.5 |
deleted 2 characters in body; edited tags
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| Feb 19, 2011 at 17:09 | history | asked | Michał Oszmaniec | CC BY-SA 2.5 |