Loop-Erasure of Plane Brownian Motion

Details Loop-Erasure of Plane Brownian Motion Loop-Erasure of Plane Brownian Motion

2010-01-19

arxiv.org/abs/1001.3189v1

Mathematics

Probability

10 pages

Scientific paper

We use the coupling technique to prove that there exists a loop-erasure of a
plane Brownian motion stopped on exiting a simply connected domain, and the
loop-erased curve is the reversal of a radial SLE$_2$ curve.

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