On the critical value function in the divide and color model
Artikel i vetenskaplig tidskrift, 2013

The divide and color model on a graph G arises by first deleting each edge of G with probability 1-p independently of each other, then coloring the resulting connected components (i.e., every vertex in the component) black or white with respective probabilities r and 1-r, independently for different components. Viewing it as a (dependent) site percolation model, one can denote the critical point r^G_c(p). In this paper, we mainly study the continuity properties of the function r^G_c, which is an instance of the question of locality for percolation. Our main result is the fact that in the case G=Z^2, r^G_c is continuous on the interval [0,1/2); we also prove continuity at p=0 for the more general class of graphs with bounded degree. We then investigate the sharpness of the bounded degree condition and the monotonicity of r^G_c(p) as a function of p.


critical value

divide and color model

stochastic domination



András Bálint

Chalmers, Tillämpad mekanik, Fordonssäkerhet

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Vehicle and Traffic Safety Centre at Chalmers

Vincent Beffara

Vincent Tassion


1980-0436 (ISSN)

Vol. 10 2 653-666


Grundläggande vetenskaper


Annan fysik

Sannolikhetsteori och statistik

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