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

@inproceedings{Bollobs2014SubcriticalUP, 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}, year={2014} }

- Published 2014

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