语言动力学中的一致性与有序性
Consensus and ordering in language dynamics
摘要：
我们考虑两个社会共识模型，AB模型和限制到两个公约，它描述了人口的互动代理，可以在两个等价的状态（A或B）或在第三个混合（AB）状态。AB状态是在语言竞争和语言涌现的背景下提出的，分别与双语和同义相关。我们表明，这两个模型是等效的平均场近似，虽然在微观层面上的差异有非平凡的后果。为了指出这一点，我们研究了这些动力学的扩展，其中考虑了信心/信任，重点是一个基本的全连通图的情况下，我们表明，在AB模型中没有观察到的共识极化相变发生在博弈中。然后，我们考虑在规则晶格中的界面运动。定性地说，这两个模型表现出相同的行为：在一维晶格中的扩散界面运动，和一个曲率驱动的动态扩散条纹状亚稳态在二维之一。然而，在比较的竞争游戏中，AB-模型的动态显示，以减缓这种配置的扩散。
英文摘要：
We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.
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