# 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
Type de document :
Pré-publication, Document de travail
2013
Domaine :
Liste complète des métadonnées

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00843512
Contributeur : Vincent Beffara <>
Soumis le : jeudi 11 juillet 2013 - 15:07:17
Dernière modification le : jeudi 11 janvier 2018 - 06:12:31

### Identifiants

• 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. 2013. 〈ensl-00843512〉

### Métriques

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