Rumour Processes on N

TL;DR

This paper analyzes four stochastic models of rumor spreading on the natural numbers, focusing on conditions that determine whether the rumor reaches infinitely many individuals based on individual behaviors and probabilities.

Contribution

It introduces four new discrete-time stochastic systems modeling rumor spread with individual roles and analyzes conditions for infinite rumor propagation.

Findings

Conditions for positive probability of infinite rumor spread

Impact of individual behavior distributions on spreading

Comparison of different rumor spreading models

Abstract

We study four discrete time stochastic systems on $\bbN$ modeling processes of rumour spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumour. The appetite in spreading or hearing the rumour is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand - based on those random variables distribution - whether the probability of having an infinite set of individuals knowing the rumour is positive or not.