The sharp threshold for the Duarte model

• Béla Bollobás ^[1] ; Hugo Duminil-Copin ^[2] ; Robert Morris ^[3] ; Paul Smith ^[4]
  1. [1] University of Cambridge

     University of Cambridge

     Cambridge District, Reino Unido

     
  2. [2] Université de Genève

     Université de Genève

     Genève, Suiza

     
  3. [3] Instituto Nacional de Matemática Pura e Aplicada

     Instituto Nacional de Matemática Pura e Aplicada

     Brasil

     
  4. [4] Tel Aviv University

     Tel Aviv University

     Israel

     

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 2, 2017, págs. 4222-4272
• Idioma: inglés
• DOI: 10.1214/16-AOP1163
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• Resumen

  • The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollobás, 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.