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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Global survival of branching random walks and tree-like branching random walks

Autor(es):
Bertacchi, Daniela ; Coletti, Cristian F. ; Zucca, Fabio
Número total de Autores: 3
Tipo de documento: Artigo Científico
Fonte: ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS; v. 14, n. 1, p. 381-402, 2017.
Citações Web of Science: 0
Resumo

The reproduction speed of a continuous-time 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 K-w. We provide here new sufficient conditions which guarantee that the global critical parameter equals 1/K-w. 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 lambda(w) = 1/K-w were known; here we provide an example where lambda(w) > 1/K-w. (AU)

Processo FAPESP: 15/20110-0 - Passeios Aleatórios com Ramificação e Sistemas de Partículas em Ambiente Aleatório.
Beneficiário:Cristian Favio Coletti
Linha de fomento: Bolsas no Exterior - Pesquisa