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


stochastic domination

divide and color model

critical value



András Bálint

Vehicle and Traffic Safety Centre at Chalmers

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Chalmers, Applied Mechanics, Vehicle Safety

Vincent Beffara

Vincent Tassion


1980-0436 (ISSN)

Vol. 10 2 667-679


Basic sciences

Subject Categories

Other Physics Topics

Probability Theory and Statistics

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