Reflected planar Brownian motions, intertwining relations and crossing probabilities
arXiv:math/0302250 · doi:10.1016/j.anihpb.2003.11.005
Abstract
Prompted by an example arising in critical percolation, we study some reflected Brownian motions in symmetric planar domains and show that they are intertwined with one-dimensional diffusions. In the case of a wedge, the reflected Brownian motion is intertwined with the 3-dimensional Bessel process. This implies some simple hitting distributions and sheds some light on the formula proposed by Watts for double-crossing probabilities in critical percolation.
18 pages, 5 figures