2015/10/09 by Junior, Valdivino Vargas, Fábio P. Machado, Machado, Fábio Prates +2
Mathematics · Physics and Astronomy · #60G50 #60K35 #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1510.02821
openalex publication_date 2015/10/09 · openalex created_date 2017/03/03 · openalex updated_date 2026/07/28
We study a rumour model from a percolation theory and branching process point of view. The existence of a giant component is related to the event where the rumour, which started from the root of a tree, spreads out through an infinite number of its vertices. We present lower and upper bounds for the probability of that event, according to the distribution of the random variables that defines the radius of influence of each individual. We work with Galton-Watson branching trees (homogeneous and non-homogeneous) and spherically symmetric trees which includes homogeneous and k-periodic trees.