Abstract
In modified two-neighbour bootstrap percolation in two dimensions each site of is initially independently infected with probability p and on each discrete time step one additionally infects sites with at least two non-opposite infected neighbours. In this note we establish that for this model the second term in the asymptotics of the infection time τ unexpectedly scales differently from the classical two-neighbour model, in which arbitrary two infected neighbours are required. More precisely, we show that for modified bootstrap percolation with high probability as it holds that
for some positive constant c, while the classical model is known to lack the logarithmic factor.
Funding Statement
Supported by the Austrian Science Fund (FWF): P35428-N and ERC Starting Grant 680275 “MALIG.”
Acknowledgments
We thank Augusto Teixeira for several enlightening discussions and IMPA, where this work was initiated, for the hospitality.
Citation
Ivailo Hartarsky. "Sensitive bootstrap percolation second term." Electron. Commun. Probab. 28 1 - 7, 2023. https://doi.org/10.1214/23-ECP535
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