发表机构
University of São Paulo; Arizona State University; Federal University of Minas Gerais（圣保罗大学; 亚利桑那州立大学; 米纳斯吉拉斯联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入Λ-广播选民模型，推广经典选民模型至多重意见传播，通过协调合并随机游走对偶系统，刻画了平稳测度的极值性、矩依赖性与连续性，并在树和Z^d上给出完整分类。
AI 中文摘要
经典选民模型与合并随机游走是对偶的，正如Kingman合并子通过二元合并描述谱系一样。受从Kingman合并子到允许多重合并的Λ-合并子的过渡启发，我们引入了Λ-广播选民模型，在该模型中，一个选民可以根据由[0,1]上的有限测度Λ所支配的机制，同时将其意见传播给多个邻居；当Λ=δ_0时，经典选民模型得以恢复。我们证明了该模型在有界度的一般图上是良定义的，并构造了一族由有界调和函数参数化的平稳测度μ_{α,Λ}，这些测度根据底层随机游走的有限或无限碰撞性质来刻画极值平稳测度。然后，我们通过有限个矩研究了平稳测度对广播测度Λ的依赖性。我们给出了不同矩轮廓产生不同平稳测度的一般条件，并特别在有界度的树以及最近邻Z^d（d≥3）上获得了完整刻画。我们还证明了平稳测度关于矩轮廓的连续性。我们的主要工具是一个协调合并随机游走的对偶系统，其单个粒子是简单随机游走，但可以同时跳跃和合并；与独立随机游走的耦合使我们能够将其长期行为与普通随机游走的碰撞性质联系起来。
英文摘要
The classical voter model is dual to coalescing random walks, in much the same way that the Kingman coalescent describes genealogies through binary mergers. Motivated by the passage from the Kingman to the~\(Λ\)-coalescent, where multiple mergers are allowed, we introduce the~\(Λ\)-broadcast voter model, in which a voter may transmit its opinion simultaneously to several neighbors according to a mechanism governed by a finite measure~\(Λ\) on~\([0,1]\); the classical voter model is recovered when~\(Λ=δ_0\). We show that our model is well-defined on general graphs with bounded degrees, and we construct a family of stationary measures~\({μ_{α,Λ}}\), parametrized by bounded harmonic functions, that characterize the extremal stationary measures according to the finite or infinite collision property of the underlying random walk. We then study the dependence of the stationary measures on the broadcasting measure $Λ$ through a finite number of its moments. We give general conditions under which different moment profiles yield different stationary measures and obtain, in particular, a complete characterization on trees with bounded degrees and on nearest-neighbour~\(\mathbb Z^d\),~\(d\ge3\). We also prove continuity of the stationary measures with respect to the moment profile. Our main tool is a dual system of coordinated coalescing random walks, whose individual particles are simple random walks but which may jump and coalesce simultaneously; a coupling with independent random walks allows us to relate their long-time behaviour to ordinary random walk collision properties.
