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

Journal article, 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