The harmonic explorer and its convergence to SLE(4)
概率论
2008-11-26 v3 数学物理
复变函数
math.MP
摘要
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.
引用
@article{arxiv.math/0310210,
title = {The harmonic explorer and its convergence to SLE(4)},
author = {Oded Schramm and Scott Sheffield},
journal= {arXiv preprint arXiv:math/0310210},
year = {2008}
}
备注
Published at http://dx.doi.org/10.1214/009117905000000477 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)