Timeline for Random walk on a simple finite network
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 21, 2011 at 20:45 | vote | accept | Michał Oszmaniec | ||
| Feb 20, 2011 at 21:52 | comment | added | Omer | I don't see right now a way to deal with the perturbed lattice. If we can show that the probability of hitting either end of the weak edge from before $D$ is larger from $q$ than from $p$ then it seems like a path decomposition argument might work. This in turn boils down to comparing values of the Green's function for the RW in the given domain, killed at $D$. | |
| Feb 20, 2011 at 8:30 | comment | added | Michał Oszmaniec | Thanks a lot! That is a rally cool argument! I was thinking about generalization of this result - consider a perturbation introduced into a network (see picasaweb.google.com/Michal.Oszmaniec/Math#5575684413855038498 ) that is located "directly above" considered points $p$ and $q$. Perturbation decreases transition probability of passage trough the edge it occupies (in both directions). Will the relation between $\mathbb{P}(p)$ and $\mathbb{P}(q)$ still hold? | |
| Feb 19, 2011 at 23:11 | comment | added | George Lowther | +1. Very nice argument! | |
| Feb 19, 2011 at 22:55 | history | answered | Omer | CC BY-SA 2.5 |