Subcritical U-bootstrap Percolation Models Have Non-trivial Phase Transitions

  title={Subcritical U-bootstrap Percolation Models Have Non-trivial Phase Transitions},
  author={B{\'e}la Bollob{\'a}s and MICHA L PRZYKUCKI and P. N. Smith},
We prove that there exist natural generalizations of the classical bootstrap percolation model on Z that have non-trivial critical probabilities, and moreover we characterize all homogeneous, local, monotone models with this property. Van Enter [28] (in the case d = r = 2) and Schonmann [25] (for all d > r > 2) proved that r-neighbour bootstrap percolation models have trivial critical probabilities on Z for every choice of the parameters d > r > 2: that is, an initial set of density p almost… CONTINUE READING


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