2:33 AM
@Bellatrix Why would that be surprising - after all the comments are displayed to everybody.
Just a minor nitpick regarding your recent edit - it's Jyrki and not Jirky.

6 hours later…
8:20 AM
Following one looks interesting and somehow ignored, but I don't know how easy or hard the question is (i dont have any expertise on markov chains)
3

Suppose there is a grid $[1,N]^2$. A person standing at some initial point $(x_0,y_0)$ walk randomly within the grid. At each location, he/she walks to a neighboring location with equal probability (e.g., for an interior point, the probability is $\frac{1}{4}$; for a corner, it's $\frac{1}{2}$.)....

Although now looking at it, the barriers in the question are arbitrary, so it is probably too hard... (it might be more answerable question if the barriers were at the border)

9 hours later…
4:54 PM
room topic changed to Pearl Dive: A meeting place for sponsors and excellent posts. See math.meta.stackexchange.com/q/31105/11619 (no tags)
@Sil I will wait for more opinions. I recall a similar but simpler problem from IMO training 40 years ago. It was about a cube with vertices connected by wires, and and an ant walking about randomly, unaware of glue in two specified vertices. That is a much more symmetrical variant. And the question was only about the probabilities of which trap that the ant is gonna get caught on (given the starting vertex).
Anyway, I'm sure there are answerable variants of that question. No clue about the general one.
Too bad Did is no longer around :-( He could weigh in.