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Jul 28, 2016 at 18:59 comment added Christian Remling You certainly need a two-dimensional Brownian motion for the usual connection to harmonic measure (a $1$-dimensional BM started in a gap can of course only hit the left or right endpoint of the gap).
Jul 28, 2016 at 7:53 comment added Bjørn Kjos-Hanssen (Not sure about this, though.)
Jul 28, 2016 at 7:49 history answered Bjørn Kjos-Hanssen CC BY-SA 3.0