Limit theorems for a general stochastic rumour model

TL;DR

This paper develops a comprehensive stochastic rumour model that generalizes classical models by including uninterested individuals and various meeting rates, and establishes fundamental limit theorems for the model.

Contribution

It introduces a unified framework for rumour spreading models and proves law of large numbers and central limit theorems for the model's proportions.

Findings

Law of Large Numbers for the model

Central Limit Theorem for proportions

Generalization of classical rumour models

Abstract

We study a general stochastic rumour model in which an ignorant individual has a certain probability of becoming a stifler immediately upon hearing the rumour. We refer to this special kind of stifler as an uninterested individual. Our model also includes distinct rates for meetings between two spreaders in which both become stiflers or only one does, so that particular cases are the classical Daley-Kendall and Maki-Thompson models. We prove a Law of Large Numbers and a Central Limit Theorem for the proportions of those who ultimately remain ignorant and those who have heard the rumour but become uninterested in it.