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

Artikel i vetenskaplig tidskrift, 2013

We obtain condence intervals for the location of the percolation phase transition in Häggström's divide and color model on the square lattice Z^2 and the hexagonal lattice 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 Z^2 and H and enable a comparison with the triangular lattice 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

Percolation

stochastic domination

divide and color model

critical value

locality