The cone percolation model on Galton-Watson and on spherically symmetric trees

TL;DR

This paper analyzes a rumor spreading model on different types of trees using percolation theory and branching processes, providing bounds on the probability of widespread rumor dissemination.

Contribution

It introduces bounds for the probability of a rumor reaching infinitely many vertices on Galton-Watson and spherically symmetric trees, expanding understanding of influence spread models.

Findings

Derived lower and upper bounds for spreading probability

Applied bounds to Galton-Watson and spherically symmetric trees

Enhanced understanding of influence spread in tree structures

Abstract

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.