Galton-Watson processes in varying environment and accessibility percolation

Autor(es)

Bertacchi, Daniela ^[1] ; Rodriguez, Pablo M. ^[2] ; Zucca, Fabio ^[3]

Afiliação do(s) autor(es)

^[1] Univ Milano Bicocca, Via Cozzi 53, I-20125 Milan - Italy

^[2] Univ Sao Paulo, Ave Trabalhador Sao Carlense 400, BR-13560590 Sao Carlos, SP - Brazil

^[3] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan - Italy

• Tipo de documento: Artigo Científico
• Fonte: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 34, n. 3, p. 613-628, AUG 2020.
• Citações Web of Science: 0

Resumo

This paper deals with branching processes in varying environment with selection, where the offspring distribution depends on the generation and every particle has a random fitness which can only increase along genealogical lineages (descendants with small fitness do not survive). We view the branching process in varying environment (BPVE) as a particular example of branching random walk. We obtain conditions for the survival or extinction of a BPVE (with or without selection), using fixed point techniques for branching random walks. These conditions rely only on the first and second moments of the offspring distributions. Our results can be interpreted in terms of accessibility percolation on Galton-Watson trees. In particular, we obtain that there is no accessibility percolation on almost every Galton-Watson tree where the expected number of offspring grows sublinearly in time, while superlinear growths allows percolation. This result is in agreement with what was found for deterministic trees in Nowak and Krug (Europhysics Letters 101 (2013) 66004). (AU)

• Processo FAPESP: 16/11648-0 - Teoremas limite e resultados de transição de fase para modelos de propagação de informação em grafos
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 15/03868-7 - Comportamento assintótico de processos estocásticos em grafos e aplicações
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático