Harmonic explorer and its convergence to SLE4
Harmonic explorer and its convergence to SLE4
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DOI：
10.1214/009117905000000477
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发表时间：
2003-10
影响因子：
2.3
通讯作者：
O. Schramm;S. Sheffield
中科院分区：
文献类型：
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作者：
O. Schramm;S. Sheffield
谐波探索者是一个随机的网格路径。非常粗略地说，在每一步中，谐波探索者向右转一次，其概率等于路径左侧从当前路径末端附近的点开始的离散谐波测度。我们证明了谐波探索者随着网格的细化收敛到SLE 4。
The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left-hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE 4 as the grid gets finer.