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Confidence intervals for the critical value 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. 667-679.
[Artikel, refereegranskad vetenskaplig]

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

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



Denna post skapades 2013-12-20. Senast ändrad 2015-02-13.
CPL Pubid: 190336

 

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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