论文标题
超临界网络上的话语选民模型
Discursive Voter Models on the Supercritical Scale-Free Network
论文作者
论文摘要
选民模型是一个经典的互动粒子系统，对本地模仿方式进行了建模。我们分析当基础结构是一个无尺度的不均匀随机图时，在该图具有巨大组件的高边缘密度制度中，分析了特定选民模型的共识时间。在这个制度中，我们验证了共识的多项式顺序与[Moinet等，2018]中的平均场近似值一致。 这个“话语”模型家族具有对称的相互作用，可以更好地进行模型讨论，并由温度参数索引，温度参数对于网络程度分布的某些参数而言，被认为会产生两个不同的共识速度阶段。我们的证明依靠众所周知的二元性来融合随机步行，并使用已知的Erdős-rényi巨型子图的快速混合，对这些步行的混合时间进行控制。与亚临界情况[Fernley和Ortgiese，2022]不同，它需要限制度分布的尾指数$τ= 1+1/γ> 3 $以及低边缘密度，在巨大的组件情况下，我们还解决了“ Ultrasmall World World” Power Laws opter Laws offentent $τττ\ in（2,3] $。
The voter model is a classical interacting particle system, modelling how global consensus is formed by local imitation. We analyse the time to consensus for a particular family of voter models when the underlying structure is a scale-free inhomogeneous random graph, in the high edge density regime where this graph features a giant component. In this regime, we verify that the polynomial orders of consensus agree with those of their mean-field approximation in [Moinet et al., 2018]. This "discursive" family of models has a symmetrised interaction to better model discussions, and is indexed by a temperature parameter which, for certain parameters of the power law tail of the network's degree distribution, is seen to produce two distinct phases of consensus speed. Our proofs rely on the well-known duality to coalescing random walks and a control on the mixing time of these walks, using the known fast mixing of the Erdős-Rényi giant subgraph. Unlike in the subcritical case [Fernley and Ortgiese, 2022] which requires tail exponent of the limiting degree distribution $τ=1+1/γ>3$ as well as low edge density, in the giant component case we also address the "ultrasmall world" power law exponents $τ\in (2,3]$.
