The reproduction speed of a continuous-time branching random walk is proportional to a positive parameter λ. There is a threshold for λ, which is called λw, that separates almost sure global extinction from global survival. Analogously, there exists another threshold λs below which any site is visited almost surely a finite number of times (i.e. local extinction) while above it there is a positive probability of visiting every site infinitely many times. The local critical parameter λs is completely understood and can be computed as a function of the reproduction rates. On the other hand, only for some classes of branching random walks it is known that the global critical parameter λw is the inverse of a certain function of the reproduction rates, which we denote by Kw. We provide here new sufficient conditions which guarantee that the global critical parameter equals 1/Kw. This result extends previously known results for branching random walks on multigraphs and general branching random walks. We show that these sufficient conditions are satisfied by periodic tree-like branching random walks. We also discuss the critical parameter and the critical behaviour of continuous-time branching processes in varying environment. So far, only examples where λw = 1/Kw were known; here we provide an example where λw > 1/Kw.
Bertacchi, D., Coletti, C., & Zucca, F. (2017). Global survival of branching random walks and tree-like branching random walks. ALEA, 14(1), 381-402.
Citazione: | Bertacchi, D., Coletti, C., & Zucca, F. (2017). Global survival of branching random walks and tree-like branching random walks. ALEA, 14(1), 381-402. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | Si |
Titolo: | Global survival of branching random walks and tree-like branching random walks |
Autori: | Bertacchi, D; Coletti, C; Zucca, F |
Autori: | |
Data di pubblicazione: | 2017 |
Lingua: | English |
Rivista: | ALEA |
Digital Object Identifier (DOI): | http://dx.doi.org/10.30757/alea.v14-21 |
Appare nelle tipologie: | 01 - Articolo su rivista |
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