PERCOLATION ON A PRODUCT OF TWO TREES

• 成果类型: Article
• 署名作者: Kozma, Gady
• 署名单位: Weizmann Institute of Science
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP618
• 发表日期: 2011
• 页码: 1864-1895
• 关键词: mean-field criticality; non-amenable graphs; critical-behavior; triangle condition; PHASE-TRANSITION; exponents; sharpness; models

摘要

We show that critical percolation on a product of two regular trees of degree >= 3 satisfies the triangle condition. The proof does not examine the degrees of vertices and is not perturbative in any sense. It relies on an unpublished lemma of Oded Schramm.