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- W3089207841 abstract "Consider a $p$-random subset $A$ of initially infected vertices in the discrete cube $[L]^{3}$, and assume that the neighborhood of each vertex consists of the $a_{i}$ nearest neighbors in the $pm e_{i}$-directions for each $iin {1,2,3}$, where $a_{1}le a_{2}le a_{3}$. Suppose we infect any healthy vertex $xin [L]^{3}$ already having $a_{3}+1$ infected neighbors, and that infected sites remain infected forever. In this paper, we determine the critical length for percolation up to a constant factor in the exponent, for all triples $(a_{1},a_{2},a_{3})$. To do so, we introduce a new algorithm called the beams process and prove an exponential decay property for a family of subcritical two-dimensional bootstrap processes." @default.
- W3089207841 created "2020-10-01" @default.
- W3089207841 creator A5021447357 @default.
- W3089207841 date "2020-09-01" @default.
- W3089207841 modified "2023-10-16" @default.
- W3089207841 title "Anisotropic bootstrap percolation in three dimensions" @default.
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- W3089207841 doi "https://doi.org/10.1214/20-aop1434" @default.
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