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

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
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Journal articles
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Cited literature [14 references]

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00843512
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Submitted on : Wednesday, January 24, 2018 - 2:15:07 PM
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Balint2013a.pdf
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### Identifiers

• HAL Id : ensl-00843512, version 1
• ARXIV : 1307.2755

### Citation

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, Instituto Nacional de Matemática Pura e Aplicada, 2013, 10 (2), pp.667-679. ⟨ensl-00843512⟩

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