ON MONOCHROMATIC ARM EXPONENTS FOR 2D CRITICAL PERCOLATION

• 成果类型: Article
• 署名作者: Beffara, Vincent; Nolin, Pierre
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); New York University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP581
• 发表日期: 2011
• 页码: 1286-1304
• 关键词: brownian intersection exponents; plane; VALUES

摘要

We investigate the so-called monochromatic arm exponents for critical percolation in two dimensions. These exponents, describing the probability of observing j disjoint macroscopic paths, are shown to exist and to form a different family from the (now well understood) polychromatic exponents. More specifically, our main result is that the monochromatic j-arm exponent is strictly between the polychromatic j-arm and (j + 1)-arm exponents.