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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.)

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

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Coletti, Cristian F. [1] ; Gava, Renato J. [2] ; Rodriguez, Pablo M. [3]
Total Authors: 3
[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
Total Affiliations: 3
Document type: Journal article
Web of Science Citations: 1

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)

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: 13/03898-8 - Stochastic modeling of information difusion on interacting systems
Grantee:Pablo Martin Rodriguez
Support Opportunities: Regular Research Grants
FAPESP's process: 15/20110-0 - Branching Random Walks and Interacting particle System in Random Environment.
Grantee:Cristian Favio Coletti
Support Opportunities: Scholarships abroad - Research