The Maki-Thompson rumor model on infinite Cayley trees

随机谣言模型中传播者的最大比例

The maximum proportion of spreaders in stochastic rumor models

本文研究广义随机谣言模型，包含 Daley--Kendall 和 Maki--Thompson 模型的概率变体，证明了种群规模趋于无穷时传播者最大比例的几乎必然收敛性，并得出经典模型中谣言峰值的渐近比例为 0.3069。

具有随机知晓率的 Maki-Thompson 模型

The Maki-Thompson model with random awareness

本文提出一种个体状态无限的谣言传播模型，通过扩展大数定律至无限维 Markov 链进行分析，推导谣言爆发后各状态渐近比例并探讨传播波动条件。

Stochastic rumors on random trees

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 probabil…

Asymptotic behavior for a modified Maki-Thompson model with directed inter-group interactions

In this work we propose a new extension for the Maki-Thompson rumor model which incorporates inter-group directed contacts. The model is defined on an homogeneously mixing population where the existence of two differentiated groups of individuals is assumed. While individuals of one group have an active role in the spreading process, individuals of the other group only contribute in stifling the rumor provided they would contacted. For this model we measure the impact of dissemination by studying the remaining proportion of ignorants of both groups at the end of the process. In addition we dis…

The role of multiple repetitions on the size of a rumor

We propose a mathematical model to measure how multiple repetitions may influence in the ultimate proportion of the population never hearing a rumor during a given outbreak. The model is a multi-dimensional continuous-time Markov chain that can be seen as a generalization of the Maki-Thompson model for the propagation of a rumor within a homogeneously mixing population. In the well-known basic model, the population is made up of "spreaders", "ignorants" and "stiflers", and any spreader attempts to transmit the rumor to the other individuals via directed contacts. In case the contacted individu…

无限图上空间Maki–Thompson模型的灭绝、存活与波动

Extinction, Survival and Fluctuations for the Spatial Maki--Thompson Model on Infinite Graphs

该研究针对有界度无限连通图上的空间Maki–Thompson谣言模型，证明了线性增长Cayley图上谣言必然灭绝、超线性增长Cayley图上谣言可存活等结论，还得到了相关中心极限定理。