2:33 AM
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 $\frac{1}{2}$.)....
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).
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Pearl Dive
A meeting place for sponsors and excellent posts. See math.met...