We study a generalized branching random walk where particles breed at a rate which depends on the number of neighboring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population survives without exploding. We construct a nontrivial invariant measure for this case.
Publié le : 2007-08-14
Classification:
Interacting particle systems,
branching random walks,
contact process,
phase transition,
60K35
@article{1186755234,
author = {Bertacchi, Daniela and Posta, Gustavo and Zucca, Fabio},
title = {Ecological equilibrium for restrained branching random walks},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 1117-1137},
language = {en},
url = {http://dml.mathdoc.fr/item/1186755234}
}
Bertacchi, Daniela; Posta, Gustavo; Zucca, Fabio. Ecological equilibrium for restrained branching random walks. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 1117-1137. http://gdmltest.u-ga.fr/item/1186755234/