论文标题
Maki-Thompson关于无限Cayley树的谣言模型
The Maki-Thompson rumor model on infinite Cayley trees
论文作者
论文摘要
在本文中，我们研究了关于无限凯利树的Maki-Thompson谣言模型。该模型的基本版本是通过假设图表代表的人群细分为三类个体的基本版本：无知者，播种者和僵硬者。一个播种者以第一次将谣言告诉了其任何（最近的）无知的邻居。以相同的速度，播种器与其他（最近的邻居）散布器或僵硬剂接触后变为僵硬的人。在这项工作中，我们研究了该模型的无限凯利树，该模型被称为Markov连续的马尔可夫链，并将分析扩展到概括，在该概括中，每个播放器都在参与给定数量的扼杀经验后停止谣言。我们研究了足够的条件，在这些条件下，谣言要么灭绝或以积极的概率生存。
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.
