The dimension of the SLE curves

• 成果类型: Article
• 署名作者: Beffara, Vincent
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP364
• 发表日期: 2008
• 页码: 1421-1452
• 关键词: erased random-walks; conformal-invariance; critical percolation; RESTRICTION; exponents; plane

摘要

Let gamma be the curve generating a Schramm-Loewner Evolution (SLE) process, with parameter kappa >= 0. We prove that, with probability one, the Hausdorff dimension of gamma is equal to Min(2, 1 + kappa/8).