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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2013

Confidence intervals for the critical value in the divide and color model

Résumé

We obtain confidence intervals for the location of the percolation phase transition in Häggström's divide and color model on the square lattice $\mathbb{Z}^2$ and the hexagonal lattice $\mathbb{H}$. The resulting probabilistic bounds are much tighter than the best deterministic bounds up to date; they give a clear picture of the behavior of the DaC models on $\mathbb{Z}^2$ and $\mathbb{H}$ and enable a comparison with the triangular lattice $\mathbb{T}$. In particular, our numerical results suggest similarities between DaC model on these three lattices that are in line with universality considerations, but with a remarkable difference: while the critical value function $r_c(p)$ is known to be constant in the parameter $p$ for $p
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Dates et versions

ensl-00843512 , version 1 (24-01-2018)

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András Bálint, Vincent Beffara, Vincent Tassion. Confidence intervals for the critical value in the divide and color model. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2013, 10 (2), pp.667-679. ⟨ensl-00843512⟩

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