标题： 大型图上的共识与投票：图极限理论的应用 显示英文标题

标题： Consensus and Voting on Large Graphs: An Application of Graph Limit Theory

摘要： 在Medvedev(2014)最近工作的基础上，我们建立了基本共识模型——投票模型与图极限理论之间的新联系。 我们证明，在投票模型中，如果在连续极限下达成共识，则有限模型的解最终会接近一个常数函数，并确定了一类保证共识的图极限。 还证明了可以使用Janson对图极限连通性的定义，将连续极限中的动力学分解为各个连通分量上的动力学的直和。 这意味着可以不失一般性地假设连续投票模型发生在连通的图极限上。 显示英文摘要

摘要： Building on recent work by Medvedev (2014) we establish new connections between a basic consensus model, called the voting model, and the theory of graph limits. We show that in the voting model if consensus is attained in the continuum limit then solutions to the finite model will eventually be close to a constant function, and a class of graph limits which guarantee consensus is identified. It is also proven that the dynamics in the continuum limit can be decomposed as a direct sum of dynamics on the connected components, using Janson's definition of connectivity for graph limits. This implies that without loss of generality it may be assumed that the continuum voting model occurs on a connected graph limit.