The time of bootstrap percolation in two dimensions

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• 作者：Paul Balister ; Béla Bollobás ; Paul Smith
• 关键词：Bootstrap percolation ; Concentration of measure
• 刊名：Probability Theory and Related Fields
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：166
• 期：1-2
• 页码：321-364
• 全文大小：810 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Mathematical and Computational Physics
  Quantitative Finance
  Mathematical Biology
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064
• 卷排序：166

文摘

We study the distribution of the percolation time T of 2-neighbour bootstrap percolation on \([n]^2\) with initial set \(A\sim {\text {Bin}}([n]^2,p)\). We determine T up to a constant factor with high probability for all p above the critical probability for percolation, and to within a \(1+o(1)\) factor for a large range of p.