Stochastic rumors on random trees

TL;DR

This paper analyzes the spread and extinction of rumors on random trees using the Maki-Thompson model, identifying phase transitions and estimating the rumor's mean range in various random tree structures.

Contribution

It provides a new analysis of the Maki-Thompson rumor model specifically on random trees, including phase transition criteria and mean range estimates.

Findings

Existence of a phase transition for rumor survival on random trees

Estimates for the mean range of the rumor

Application to various well-known random tree models

Abstract

The Maki-Thompson rumor model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals; namely, ignorants, spreaders and stiflers. A spreader tells the rumor to any of its nearest ignorant neighbors at rate one. At the same rate, a spreader becomes a stifler after a contact with other nearest neighbor spreaders, or stiflers. In this work we study the model on random trees. As usual we define a critical parameter of the model as the critical value around which the rumor either becomes extinct almost-surely or survives with positive probability. We analyze the existence of phase-transition regarding the survival of the rumor, and we obtain estimates for the mean range of the rumor. The applicability of our results is illustrated with examples on random trees generated from some well-known discrete distributions.