一维Axelrod模型中的固定
Fixation in the one-dimensional Axelrod model
摘要：
阿克塞尔罗德模型是一个空间随机模型的动态文化，其中包括两个重要的社会因素：社会影响，个人变得更加相似，当他们互动的倾向，和同质性，个人互动的倾向，更频繁地与个人谁是更相似的。交互网络的每个顶点都以其文化为特征，这是一个$F$文化特征的向量，每个特征可以呈现$q$不同的状态。邻居对以与他们共有的文化特征数量成比例的速率进行交互，这导致交互对具有多一个共同的文化特征。在这篇文章中，我们继续分析阿克塞尔罗德模型的第一作者发起的证明，一维系统固定时，$F\leq cq$的斜率满足方程$e^{-c}=c$。此外，我们还证明了具有至少三个状态的双特征模型是固定的。这最后一个结果是尖锐的，因为它是从以前的作品，一维两个功能两个状态Axelrod模型集群已知。
英文摘要：
The Axelrod model is a spatial stochastic model for the dynamics of cultures which includes two important social factors: social influence, the tendency of individuals to become more similar when they interact, and homophily, the tendency of individuals to interact more frequently with individuals who are more similar. Each vertex of the interaction network is characterized by its culture, a vector of $F$ cultural features that can each assumes $q$ different states. Pairs of neighbors interact at a rate proportional to the number of cultural features they have in common, which results in the interacting pair having one more cultural feature in common. In this article, we continue the analysis of the Axelrod model initiated by the first author by proving that the one-dimensional system fixates when $F\leq cq$ where the slope satisfies the equation $e^{-c}=c$. In addition, we show that the two-feature model with at least three states fixates. This last result is sharp since it is known from previous works that the one-dimensional two-feature two-state Axelrod model clusters.
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