Reflected planar Brownian motions, intertwining relations and crossing probabilities
Probability
2007-05-23 v1
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.
Cite
@article{arxiv.math/0302250,
title = {Reflected planar Brownian motions, intertwining relations and crossing probabilities},
author = {Julien Dubedat},
journal= {arXiv preprint arXiv:math/0302250},
year = {2007}
}
Comments
18 pages, 5 figures