Higher order corrections for anisotropic bootstrap percolation

• 成果类型: Article
• 署名作者: Duminil-Copin, Hugo; van Enter, Aernout C. D.; Hulshof, Tim
• 署名单位: Universite Paris Saclay; University of Geneva; University of Groningen; Eindhoven University of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0808-7
• 发表日期: 2018
• 页码: 191-243
• 关键词: sharp metastability threshold; models

摘要

We study the critical probability for the metastable phase transition of the two-dimensional anisotropic bootstrap percolation model with (1, 2)-neighbourhood and threshold r = 3. The first order asymptotics for the critical probability were recently determined by the first and second authors. Here we determine the following sharp second and third order asymptotics: We note that the second and third order terms are so large that the first order asymptotics fail to approximate pc even for lattices of size well beyond 1010(1000).