Advanced search
Start date
Betweenand
Related content
(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

Full text
Author(s):
Coletti, Cristian F. [1] ; Gava, Renato J. [2] ; Rodriguez, Pablo M. [3]
Total Authors: 3
Affiliation:
[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
Source: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 492, p. 382-388, FEB 15 2018.
Web of Science Citations: 1
Abstract

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 type: Regular Research Grants
FAPESP's process: 15/20110-0 - Branching random walks and interacting particle system in random environment
Grantee:Cristian Favio Coletti
Support type: Scholarships abroad - Research
FAPESP's process: 13/03898-8 - Stochastic modeling of information difusion on interacting systems
Grantee:Pablo Martin Rodriguez
Support type: Regular Research Grants