Linear Lower Bounds for $δ_c(p)$ for a Class of 2D Self-Destructive Percolation Models

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dc.creatorBerg, J. van den
dc.creatorde Lima, B. N. B.
dc.date2007-11-22
dc.date.accessioned2026-07-07T08:44:33Z
dc.date.available2026-07-07T08:44:33Z
dc.descriptionThe self-destructive percolation model is defined as follows: Consider percolation with parameter $p > p_c$. Remove the infinite occupied cluster. Finally, give each vertex (or, for bond percolation, each edge) that at this stage is vacant, an extra chance $δ$ to become occupied. Let $δ_c(p)$ be the minimal value of $δ$, needed to obtain an infinite occupied cluster in the final configuration. This model was introduced some years ago by van den Berg and Brouwer. They showed that, for the site model on the square lattice (and a few other 2D lattices satisfying a special technical condition) that $δ_c(p)\geq\frac{(p-p_c)}{p}$. In particular, $δ_c(p)$ is at least linear in $p-p_c$. Although the arguments used by van den Berg and Brouwer look quite rigid, we show that they can be suitably modified to obtain similar linear lower bounds for $δ_c(p)$ (with $p$ near $p_c$) for a much larger class of 2D lattices, including bond percolation on the square and triangular lattices, and site percolation on the star lattice (or matching lattice) of the square lattice.
dc.identifierhttps://arxiv.org/abs/0711.3563
dc.identifierhttp://arxiv.org/abs/0711.3563
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142692
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 82B43
dc.titleLinear Lower Bounds for $δ_c(p)$ for a Class of 2D Self-Destructive Percolation Models
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