Percolation and contact processes with low-dimensional inhomogeneity

• 成果类型: Article
• 署名作者: Newman, CM; Wu, CC
• 署名单位: New York University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1023481113
• 发表日期: 1997
• 页码: 1832-1845
• 关键词: critical-behavior; models; TREE; probability; phase

摘要

We consider inhomogeneous nearest neighbor Bernoulli bond percolation on Z(d) where the bonds in a fixed s-dimensional hyperplane (1 less than or equal to s less than or equal to d - 1) have density p(1) and all other bonds have fixed density, p(c)(Z(d)), the homogeneous percolation critical value. For s greater than or equal to 2, it is natural to conjecture that there is a new critical value, p(c)(s)(Z(d)), for p(1), strictly between p(c)(Z(d)) and p(c)(Z(s)); we prove this for large d and 2 less than or equal to s less than or equal to d - 3. For s = 1, it is natural to conjecture that p(c)(1)(Z(d)) = 1, as shown for d = 2 by Zhang; we prove this for large d. Related results for the contact process are also presented.