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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.)

LOCAL AND GLOBAL SURVIVAL FOR NONHOMOGENEOUS RANDOM WALK SYSTEMS ON Z

Autor(es):
Bertacchi, Daniela [1] ; Machado, Fabio Prates [2] ; Zucca, Fabio [3]
Número total de Autores: 3
Afiliação do(s) autor(es):
[1] Univ Milano Bicocca, I-20125 Milan - Italy
[2] Univ Sao Paulo, BR-05508 Sao Paulo - Brazil
[3] Politecn Milan, Milan - Italy
Número total de Afiliações: 3
Tipo de documento: Artigo Científico
Fonte: ADVANCES IN APPLIED PROBABILITY; v. 46, n. 1, p. 256-278, MAR 2014.
Citações Web of Science: 3
Resumo

We study an interacting random walk system on Z where at time 0 there is an active particle at 0 and one inactive particle on each site n >= 1. Particles become active when hit by another active particle. Once activated, the particle starting at n performs an asymmetric, translation invariant, nearest neighbor random walk with left-jump probability l(n). We give conditions for global survival, local survival, and infinite activation both in the case where all particles are immortal and in the case where particles have geometrically distributed lifespan (with parameter depending on the starting location of the particle). More precisely, once activated, the particle at n survives at each step with probability P-n is an element of {[}0, 1]. In particular, in the immortal case, we prove a 0-1 law for the probability of local survival when all particles drift to the right. Besides that, we give sufficient conditions for local survival or local extinction when all particles drift to the left. In the mortal case, we provide sufficient conditions for global survival, local survival, and local extinction (which apply to the immortal case with mixed drifts as well). Analysis of explicit examples is provided: we describe completely the phase diagram in the cases 1/2 - l(n) similar to, +/- 1/n(alpha,) P-n= 1 and 1/2 - l(n) similar to +/- 1/n(alpha), 1 - p(n) similar to 1/n(beta)(where alpha, beta > 0). (AU)

Processo FAPESP: 09/52379-8 - Modelagem estocástica de sistemas interagentes
Beneficiário:Fabio Prates Machado
Linha de fomento: Auxílio à Pesquisa - Temático