On the existence of accessibility in a tree-indexed percolation model

Autor(es)

Coletti, Cristian F. ^[1] ; Gava, Renato J. ^[2] ; Rodriguez, Pablo M. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Abc, CMCC, Av Estados 5001, Santo Andre, SP - Brazil

^[2] Univ Fed Sao Carlos UFSCar, Dept Estat DEs, Rodovia Washington Luiz, Km 235, BR-13565905 Sao Carlos, SP - Brazil

^[3] Univ Sao Paulo, ICMC, Av Trabalhador Sao Carlense 400, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 492, p. 382-388, FEB 15 2018.
• Citações Web of Science: 1

Resumo

We study the accessibility percolation model on infinite trees. The model is defined by associating an absolute continuous random variable X-v to each vertex v of the tree. The main question to be considered is the existence or not of an infinite path of nearest neighbors v(1), v(2), v(3) ... such that X-v1, < X-v2 < X-v3 < ... and which spans the entire graph. The event defined by the existence of such path is called percolation. We consider the case of the accessibility percolation model on a spherically symmetric tree with growth function given by f(i) = f(i + 1)(alpha), where alpha > 0 is a given constant. We show that there is a percolation threshold at alpha(c) = 1 such that there is percolation if alpha > 1 and there is absence of percolation if alpha <= 1. Moreover, we study the event of percolation starting at any vertex, as well as the continuity of the percolation probability function. Finally, we provide a comparison between this model with the well known Ft record model. We also discuss a number of open problems concerning the accessibility percolation model for further consideration in future research. (C) 2017 Elsevier B.V. All rights reserved. (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: 13/03898-8 - Modelagem estocástica da difusão de uma informação em sistemas interagentes
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 15/20110-0 - Passeios Aleatórios com Ramificação e Sistemas de Partículas em Ambiente Aleatório.
• Beneficiário: Cristian Favio Coletti
• Modalidade de apoio: Bolsas no Exterior - Pesquisa