Harmonic explorer and its convergence to SLE4

• 成果类型: Article
• 署名作者: Schramm, O; Sheffield, S
• 署名单位: Microsoft; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000477
• 发表日期: 2005
• 页码: 2127-2148
• 关键词: conformal-invariance; random-walks; packings

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 SLE4 as the grid gets finer.