论文标题
在完整的两部分图上的选民模型的准平台分布
Quasi-Stationary Distributions for the Voter Model on Complete Bipartite Graphs
论文作者
论文摘要
我们将离散的选民模型视为完整的两部分图，并研究该模型的准平台分布（QSD），因为其中一个分区的大小往往是无穷大的，而另一个分区仍保持固定。我们表明，QSD弱收敛到非平凡的极限，该限制具有共识，除了“大”分区中随机数量的反对顶点。此外，我们明确计算持不同政见者人数的定律，并表明它遵循重尾的sibuya分布，具体取决于“小”分区的大小。我们的结果依赖于连续时间的选民模型与我们在本文中开发的随机步行之间众所周知的双重性的离散时间类似物。
We consider the discrete-time voter model on complete bipartite graphs and study the quasi-stationary distribution (QSD) for the model as the size of one of the partitions tends to infinity while the other partition remains fixed. We show that the QSDs converge weakly to a nontrivial limit which features a consensus with the exception of a random number of dissenting vertices in the "large" partition. Moreover, we explicitly calculate the law of the number of dissenters and show that it follows the heavy-tailed Sibuya distribution with parameter depending on the size of the "small" partition. Our results rely on a discrete-time analogue of the well-known duality between the continuous-time voter model and coalescing random walks which we develop in the paper.
