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

András Bálint; Vincent Beffara; Vincent Tassion

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

András Bálint ¹ Vincent Beffara ² Vincent Tassion ²

2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Abstract : 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

Document type :

Journal articles

Domain :

Mathematics [math] / Probability [math.PR]

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

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