an:04066101
Zbl 0653.60094
Liggett, Thomas M.
Reversible growth models on symmetric sets
EN
Probabilistic methods in mathematical physics, Proc. Taniguchi Int. Symp., Katata and Kyoto/Jap. 1985, 275-301 (1987).
1987
a
60K35 60J80
survival probability; growth models; birth rate parameter
[For the entire collection see Zbl 0633.00021.]
In Probab. Theory, Relat. Fields 74, 505-528 (1987; Zbl 0589.60081), the author expressed the survival probability of reversible growth models on \({\mathbb{Z}}\) by a variational formula derived through an application of the Dirichlet principle. The present paper generalizes this result to general symmetric sets, e.g. \({\mathbb{Z}}^ d.\) It gives upper and lower bounds for the survival probability in order to calculate the critical value and exponent of a birth rate parameter \(\lambda\).
The models show that the one-dimensional situation can be completely different from higher-dimensional ones.
Th.Eisele
Zbl 0633.00021; Zbl 0589.60081