Localization for branching random walks in random environment
We consider branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If d>=3 and the environment is "not too random", then, the total population grows as fast as its expectation with strictly positive probability. If, on the other hand, d<=2, or the environment is "random enough", then the total population grows strictly slower than its expectation almost surely. We show the equivalence between the slow population growth and a natural localization property in terms of "replica overlap". We also prove a certain stronger localization property, whenever the total population grows strictly slower than its expectation almost surely.
Year of publication: |
2009
|
---|---|
Authors: | Hu, Yueyun ; Yoshida, Nobuo |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 119.2009, 5, p. 1632-1651
|
Publisher: |
Elsevier |
Keywords: | Branching random walk Random environment Localization Phase transition |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Yoshida, Nobuo, (2014)
-
Favourite sites of transient Brownian motion
Hu, Yueyun, (1998)
-
Ray-Knight theorems related to a stochastic flow
Hu, Yueyun, (2000)
- More ...