从亚临界行为到谣言模型中难以捉摸的转变
From subcritical behavior to elusive transitions in rumor models
摘要：
谣言和信息传播是人与人之间互动的自然过程。在数学上，这在流行的Maki-Thompson模型中进行了探索，其中认为不存在相变。在这里，我们表明，二阶相变是存在于这个模型中，这是没有捕获的一阶平均场近似。此外，我们提出并探索了一个修改版本的Maki-Thompson模型，其中包括一个遗忘机制。这种修改改变了马尔可夫链的性质，从无限多个吸收状态的经典设置为一个单一的吸收状态。在实践中，这使我们能够使用大量的分析和数值方法，允许模型的特征。特别是，我们发现了一个反直觉的行为，在这些模型的亚临界制度，其中的寿命的谣言增加的传播率下降，遵循幂律关系。这意味着，即使低于临界阈值，谣言也可以存活很长时间。总之，我们的研究结果表明，谣言模型的动态行为可以比以前想象的更丰富。因此，我们希望我们的研究结果激励进一步的研究分析和数值。
英文摘要：
Rumor and information spreading are natural processes that emerge from human-to-human interaction. Mathematically, this was explored in the popular Maki-Thompson model, where a phase transition was thought to be absent. Here, we show that a second-order phase transition is present in this model which is not captured by first-order mean-field approximations. Moreover, we propose and explore a modified version of the Maki-Thompson model that includes a forgetting mechanism. This modification changes the Markov chain's nature from infinitely many absorbing states in the classical setup to a single absorbing state. In practice, this allows us to use a plethora of analytic and numeric methods that permit the models' characterization. In particular, we find a counter-intuitive behavior in the subcritical regime of these models, where the lifespan of a rumor increases as the spreading rate drops, following a power-law relationship. This means that, even below the critical threshold, rumors can survive for a long time. Together, our findings suggest that the dynamic behavior of rumor models can be much richer than previously thought. Thus, we hope that our results motivate further research both analytically and numerically.
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