Branching random walks and interacting particle system in random environment
Author(s): 
Bertacchi, Daniela
;
Coletti, Cristian F.
;
Zucca, Fabio
Total Authors: 3

Document type:  Journal article 
Source:  ALEALATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS; v. 14, n. 1, p. 381402, 2017. 
Web of Science Citations:  0 
Abstract  
The reproduction speed of a continuoustime branching random walk is proportional to a positive parameter lambda. There is a threshold for lambda, which is called lambda(w), that separates almost sure global extinction from global survival. Analogously, there exists another threshold lambda(s) 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 lambda(s) 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 lambda(w) 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 treelike branching random walks. We also discuss the critical parameter and the critical behaviour of continuoustime branching processes in varying environment. So far, only examples where lambda(w) = 1/Kw were known; here we provide an example where lambda(w) > 1/Kw. (AU)  
FAPESP's process:  15/201100  Branching random walks and interacting particle system in random environment 
Grantee:  Cristian Favio Coletti 
Support type:  Scholarships abroad  Research 