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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Galton-Watson processes in varying environment and accessibility percolation

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Author(s):
Bertacchi, Daniela [1] ; Rodriguez, Pablo M. [2] ; Zucca, Fabio [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 34, n. 3, p. 613-628, AUG 2020.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 16/11648-0 - Limit theorems and phase transition results for information propagation models on graphs
Grantee:Pablo Martin Rodriguez
Support Opportunities: Regular Research Grants
FAPESP's process: 15/03868-7 - Asymptotic behavior of stochastic processes on graphs and applications
Grantee:Pablo Martin Rodriguez
Support Opportunities: Scholarships abroad - Research
FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
Grantee:Fabio Prates Machado
Support Opportunities: Research Projects - Thematic Grants