Loop-Erasure of Planar Brownian Motion
Loop-Erasure of Planar Brownian Motion
复制标题
平面布朗运动的循环擦除
DOI：
10.1007/s00220-011-1234-9
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Dapeng Zhan
中科院分区：
文献类型：
--
作者：
Dapeng Zhan
我们利用耦合技术证明了平面布朗运动在离开单连通区域时停止的时间反转存在环擦除，且环擦除曲线是径向SLE2曲线。这一结果推广到有限连通平面区域上一定条件下的布朗运动和布朗游移，且去环曲线是一条连续的LERW曲线。
We use a coupling technique to prove that there exists a loop-erasure of the time-reversal of a planar Brownian motion stopped on exiting a simply connected domain, and that the loop-erased curve is a radial SLE2curve. This result extends to Brownian motions and Brownian excursions under certain conditioning in a finitely connected plane domain, and the loop-erased curve is a continuous LERW curve.