UNIQUENESS OF THE INFINITE COMPONENT IN A RANDOM GRAPH WITH APPLICATIONS TO PERCOLATION AND SPIN-GLASSES

• 成果类型: Article
• 署名作者: GANDOLFI, A; KEANE, MS; NEWMAN, CM
• 署名单位: New York University; Delft University of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01274266
• 发表日期: 1992
• 页码: 511-527
• 关键词: random-cluster model; CONNECTEDNESS; algorithm

摘要

We extend the theorem of Burton and Keane on uniqueness of the infinite component in dependent percolation to cover random graphs on Z(d) or Z(d) x N with long-range edges. We also study a short-range percolation model related to nearest-neighbor spin glasses on Z(d) or on a slab Z(d) x {0,..., K} and prove both that percolation occurs and that the infinite component is unique for V = Z2 x {0,1} or larger.