Am Mittwoch, 13. April 2007, um 11:15 Uhr c.t. spricht
im Hörsaal A027 über das Thema
Uniform hitting distributions for conformally invariant random planar paths
Zusammenfassung: I will present several results concerning conformally invariant random planar paths which have a uniform hitting distribution in a well-chosen triangle. I will start by showing that in every triangle, there is a unique reflected Brownian motion which, started from a given corner, hits the opposite side with the uniform distribution. By an argument due to Lawler, Schramm and Werner, locality and conformal invariance of reflected Brownian motion imply that the hitting distribution determines the law of the hull of the process at the hitting time. These results can be used to compute other characteristic distributions for the hulls of reflected Brownian motion, which can be compared with those of other local processes. As an example, I will discuss simulation results for the hull distribution of self-avoiding trails in the Brauer model. Finally, I will consider some open problems in relation to SLE.
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