In this paper we study the Maki-Thompson rumor model on infinite Cayley trees. The basic version of the model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals: 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 this model on infinite Cayley trees, which is formulated as a continuous-times Markov chain, and we extend our analysis to the generalization in which each spreader ceases to propagate the rumor right after being involved in a given number of stifling experiences. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.

中文翻译：

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无限凯莱树上的 Maki-Thompson 谣言模型

在本文中，我们研究了无限凯莱树上的 Maki-Thompson 谣言模型。该模型的基本版本是通过假设由图表示的人口细分为三类个体来定义的：无知者、传播者和扼杀者。传播者以速率 1 将谣言告知其任何（最近的）无知邻居。以同样的速度，吊具在与其他（最近的邻居）吊具或扼流器接触后变成了扼流器。在这项工作中，我们在无限凯莱树上研究了这个模型，它被表述为一个连续时间马尔可夫链，我们将我们的分析扩展到每个传播者在参与给定数量的窒息后立即停止传播谣言的概括经验。我们研究了谣言消失或以正概率存活的充分条件。