The shape theorem for the frog model
Alves, O. S. M. ; Machado, F. P. ; Popov, S. Yu.
Ann. Appl. Probab., Tome 12 (2002) no. 1, p. 533-546 / Harvested from Project Euclid
We prove a shape theorem for a growing set of simple random walks on $\mathbb{Z}^d$, known as the frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, it becomes active too. At time $0$ all particles are sleeping, except for that placed at the origin. We prove that the set of the original positions of all active particles, rescaled by the elapsed time, converges to some compact convex set.
Publié le : 2002-05-14
Classification:  Simple random walk,  subadditive ergodic theorem,  60K35,  60J10
@article{1026915614,
     author = {Alves, O. S. M. and Machado, F. P. and Popov, S. Yu.},
     title = {The shape theorem for the frog model},
     journal = {Ann. Appl. Probab.},
     volume = {12},
     number = {1},
     year = {2002},
     pages = { 533-546},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1026915614}
}
Alves, O. S. M.; Machado, F. P.; Popov, S. Yu. The shape theorem for the frog model. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp.  533-546. http://gdmltest.u-ga.fr/item/1026915614/