Hey pincopallino.

There is a theorem in 2D random walks that there is a certain probability that given that something starts at a position (x,y) it will always end up back at that position in some finite future time.

This should give you an idea of distance, but if you wanted to speak about specific intervals of time then this is a bit different.

You should be able to dig up these results by searching google for limit theorems of 2D random walks.