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On the critical value function in the divide and color model

András Bálint (Institutionen för tillämpad mekanik, Fordonssäkerhet ; Institutionen för matematiska vetenskaper, matematik ; SAFER - Fordons- och Trafiksäkerhetscentrum ) ; Vincent Beffara ; Vincent Tassion
Latin American Journal of Probability and Mathematical Statistics (1980-0436). Vol. 10 (2013), 2, p. 653-666.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Percolation, divide and color model, critical value, locality, stochastic domination



Denna post skapades 2013-12-20. Senast ändrad 2015-02-13.
CPL Pubid: 190334

 

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Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Fordonssäkerhet
Institutionen för matematiska vetenskaper, matematik (2005-2016)
SAFER - Fordons- och Trafiksäkerhetscentrum

Ämnesområden

Statistisk fysik
Sannolikhetsteori och statistik

Chalmers infrastruktur