In the threshold growth model on an integer lattice, the
occupied set grows according to a simple local rule: a site becomes occupied
iff it sees at least a threshold number of already occupied sites in its
prescribed neighborhood. In this paper, we analyze the behavior of
two-dimensional threshold growth dynamics started from a sparse Bernoulli
density of occupied sites. We explain how nucleation of rare centers, invariant
shapes and interaction between growing droplets influence the first passage
time in the supercritical case. We also briefly address scaling laws for
the critical case.
Publié le : 1996-10-14
Classification:
Shape theory,
nucleation,
first passage time,
Poisson convergence,
metastability,
60K35,
52A10
@article{1041903205,
author = {Gravner, Janko and Griffeath, David},
title = {First passage times for threshold growth dynamics on ${\bf Z}\sp
2$},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1752-1778},
language = {en},
url = {http://dml.mathdoc.fr/item/1041903205}
}
Gravner, Janko; Griffeath, David. First passage times for threshold growth dynamics on ${\bf Z}\sp
2$. Ann. Probab., Tome 24 (1996) no. 2, pp. 1752-1778. http://gdmltest.u-ga.fr/item/1041903205/