We show that the branching random walk on a Galton–Watson
tree may have one or two phase transitions, depending on the relative sizes of
the mean degree and the maximum degree. We show that there are some
Galton–Watson trees on which the branching random walk has one phase
transition while the contact process has two; this contradicts a conjecture of
Madras and Schinazi. We show that the contact process has only one phase
transition on some trees of uniformly exponential growth and bounded degree,
contradicting a conjecture of Pemantle.
Publié le : 2001-10-14
Classification:
Tree,
branching random walk,
contact process,
phase transition,
spectral radius,
60K35
@article{1015345762,
author = {Pemantle, Robin and Stacey, Alan M.},
title = {The Branching Random Walk and Contact Process on Galton-Watson and
Nonhomogeneous Trees},
journal = {Ann. Probab.},
volume = {29},
number = {1},
year = {2001},
pages = { 1563-1590},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345762}
}
Pemantle, Robin; Stacey, Alan M. The Branching Random Walk and Contact Process on Galton-Watson and
Nonhomogeneous Trees. Ann. Probab., Tome 29 (2001) no. 1, pp. 1563-1590. http://gdmltest.u-ga.fr/item/1015345762/