Cox and Durrett proved the shape theorem of epidemics and forest fires with nearest neighbor interactions. They also conjectured that the shape theorem is still true with finite range interactions. In this paper, we answer this conjecture affirmatively. The method we develop allows us also to improve the result of Zhang and Zhang for all dimension.
Publié le : 1993-10-14
Classification:
Shape theorem,
finite range interactions,
first passage percolation,
60K35
@article{1176988999,
author = {Zhang, Yu},
title = {A Shape Theorem for Epidemics and Forest Fires with Finite Range Interactions},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 1755-1781},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988999}
}
Zhang, Yu. A Shape Theorem for Epidemics and Forest Fires with Finite Range Interactions. Ann. Probab., Tome 21 (1993) no. 4, pp. 1755-1781. http://gdmltest.u-ga.fr/item/1176988999/