Summary
We find the exact rate of decay for the probability that a large cube is not internally spanned for the modified bootstrap percolation. It is proven that for cubes of large side the event that the cube is not internally spanned is essentially the same as the event that the cube possesses a completely vacant line.
References
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Research partially supported by NSF DMS 9157461 and a grant from the Sloan Foundation
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Mountford, T.S. Rates for the probability of large cubes being non-internally spanned in modified bootstrap percolation. Probab. Th. Rel. Fields 93, 159–167 (1992). https://doi.org/10.1007/BF01195227
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DOI: https://doi.org/10.1007/BF01195227
Mathematics Subject Classification
- 60 K 35