具有淬火无序的选民模型中的持续个体偏差
Persistent individual bias in a voter model with quenched disorder
摘要：
许多关于选举人模型（或其变体）的理论研究都涉及总体平均的序参量。虽然这些数量很有启发性，但可能会掩盖只有在个人层面上才明显的重要统计特征。在这项工作中，我们问，哪些因素有助于一个单一的选民保持长期的统计偏见的一种意见，在面对社会影响。为此，提出了一个修改版本的网络选民模型，它也纳入了淬火无序的相互作用强度之间的个人和对抗关系的可能性。我们发现，一个稀疏的互动网络和异质性的互动强度引起的可能性，任意长期存在的个人偏见，即使没有人口平均偏见的一个意见。这是证明通过计算的特征值谱的加权网络拉普拉斯使用稀疏随机矩阵的理论。
英文摘要：
Many theoretical studies of the voter model (or variations thereupon) involve order parameters that are population-averaged. While enlightening, such quantities may obscure important statistical features that are only apparent on the level of the individual. In this work, we ask which factors contribute to a single voter maintaining a long-term statistical bias for one opinion over the other in the face of social influence. To this end, a modified version of the network voter model is proposed, which also incorporates quenched disorder in the interaction strengths between individuals and the possibility of antagonistic relationships. We find that a sparse interaction network and heterogeneity in interaction strengths give rise to the possibility of arbitrarily long-lived individual biases, even when there is no population-averaged bias for one opinion over the other. This is demonstrated by calculating the eigenvalue spectrum of the weighted network Laplacian using the theory of sparse random matrices.
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