Reflected planar Brownian motions, intertwining relations and crossing probabilities

Details Reflected planar Brownian motions, intertwining relations and crossing probabilities Reflected planar Brownian motions, intertwining relations and crossing probabilities

2003-02-20

arxiv.org/abs/math/0302250v1

Ann. Inst. H. Poincar\'e Probab. Statist. 40 (2004), no. 5, 539--552

Mathematics

Probability

18 pages, 5 figures

Scientific paper

10.1016/j.anihpb.2003.11.005

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.

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