01-247 R. Cerf, F. Manzo

The threshold regime of finite volume bootstrap percolation. (49K, LaTeX) Jul 6, 01

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Abstract. We prove that the threshold regime for bootstrap percolation in a $d$-dimensional box of diameter $L$ with parameters $p$ and $\ell$, where $3 \le \ell \le d$, is $L \sim \eexp{(\ell -1)} (C p^{-1/(d-\ell +1)})$, where $\eexp{(\ell -1)}$ is the exponential iterated $\ell-1 $ times and $C$ is bounded from above and from below by two positive constants depending on $d$, $\ell$ only.

Files: 01-247.src( 01-247.keywords , boot18.tex )