UNIVERSALITY FOR BOND PERCOLATION IN TWO DIMENSIONS

• 成果类型: Article
• 署名作者: Grimmett, Geoffrey R.; Manolescu, Joan
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP740
• 发表日期: 2013
• 页码: 3261-3283
• 关键词: thresholds; exponents

摘要

All (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices belong to the same universality class, in the sense that they have identical critical exponents at the critical point (assuming the exponents exist). This is proved using the star triangle transformation and the box-crossing property. The exponents in question are the one-arm exponent rho, the 2j-alternating-arms exponents rho(2j) for j >= 1, the volume exponent delta, and the connectivity exponent eta. By earlier results of Kesten, this implies universality also for the near-critical exponents beta, gamma, nu, Delta (assuming these exist) for any of these models that satisfy a certain additional hypothesis, such as the homogeneous bond percolation models on these three lattices.