The time of bootstrap percolation in two dimensions

We study the distribution of the percolation time T of 2-neighbour bootstrap percolation on [ n ] 2 with initial set A ∼ 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...

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Bibliographic Details
Published in:Probability theory and related fields 2016-10, Vol.166 (1-2), p.321-364
Main Authors: Balister, Paul, Bollobás, Béla, Smith, Paul
Format: Article
Language:English
Subjects:
Bootstrap method
Constants
Economics
Finance
Infections
Insurance
Management
Mathematical analysis
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Percolation
Phase transitions
Probability
Probability theory
Probability Theory and Stochastic Processes
Quantitative Finance
Random variables
Statistics for Business
Studies
Texts
Theoretical
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Summary:We study the distribution of the percolation time T of 2-neighbour bootstrap percolation on [ n ] 2 with initial set A ∼ 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 .
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-015-0657-1