Almost sure multifractal spectrum for the tip of an SLE curve

• 成果类型: Article
• 署名作者: Viklund, Fredrik Johansson; Lawler, Gregory F.
• 署名单位: Columbia University; University of Chicago; University of Chicago
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-012-0087-1
• 发表日期: 2012
• 页码: 265-322
• 关键词: brownian intersection exponents; erased random-walks; conformal-invariance; VALUES; plane

摘要

The tip multifractal spectrum of a 2-dimensional curve is one way to describe the behavior of the uniformizing conformal map of the complement near the tip. We give the tip multifractal spectrum for a Schramm-Loewner evolution (SLE) curve, we prove that the spectrum is valid with probability 1, and we give applications to the scaling of harmonic measure at the tip.