THE SHARP THRESHOLD FOR THE DUARTE MODEL

• 成果类型: Article
• 署名作者: Bollobas, Bela; Duminil-Copin, Hugo; Morris, Robert; Smith, Paul
• 署名单位: University of Cambridge; University of Memphis; University of Geneva; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Tel Aviv University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1163
• 发表日期: 2017
• 页码: 4222-4272
• 关键词: 2-dimensional bootstrap percolation; cellular-automata; metastability threshold; 3 dimensions

摘要

The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollobas, Smith and Uzzell, and the critical threshold for percolation was determined up to a constant factor for all such models by the authors of this paper. Here, we develop and refine the techniques introduced in that paper in order to determine a sharp threshold for the Duarte model. This resolves a question of Mountford from 1995, and is the first result of its type for a model with drift.