LOCAL WEAK CONVERGENCE AND PROPAGATION OF ERGODICITY FOR SPARSE NETWORKS OF INTERACTING PROCESSES
LOCAL WEAK CONVERGENCE AND PROPAGATION OF ERGODICITY FOR SPARSE NETWORKS OF INTERACTING PROCESSES
复制标题
交互过程稀疏网络的局部弱收敛和遍历性传播
DOI：
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Wu Ruoyu
中科院分区：
文献类型：
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作者：
D. Lacker;K. Ramanan;Wu Ruoyu
.我们研究了由大型稀疏图索引的相互作用粒子系统的极限行为，这些图根据离散时间马尔可夫链或离散时间马尔可夫链演化，其中粒子仅与图中最近的邻居直接相互作用。为了编码稀疏性，我们在标记（随机）图的局部弱收敛框架中工作。我们证明了粒子系统的联合律随底层图的局部弱收敛而连续变化。此外，我们还证明了全局经验测度收敛到一个非随机极限，而对于包括稀疏Erd Eros-R ′ enyi图和配置模型在内的一大类图序列，一致随机顶点的连通分量的经验测度收敛到一个随机极限。最后，在一个格子（或更一般的顺从凯莱图），我们表明，如果粒子系统的初始配置是一个平稳的遍历随机场，那么粒子轨迹的配置是任何固定的时间，一种现象，我们称之为“遍历性的传播”。沿着的方式，我们发展了一些一般性的结果，局部弱收敛的吉布斯措施的唯一性制度，这似乎是新的。
. We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest neighbors in the graph. To encode sparsity we work in the framework of local weak convergence of marked (random) graphs. We show that the joint law of the particle system varies continuously with respect to local weak convergence of the underlying graph. In addition, we show that the global empirical measure converges to a non-random limit, whereas for a large class of graph sequences including sparse Erd˝os-R´enyi graphs and configuration models, the empirical measure of the connected component of a uniformly random vertex converges to a random limit. Finally, on a lattice (or more generally an amenable Cayley graph), we show that if the initial configuration of the particle system is a stationary ergodic random field, then so is the configuration of particle trajectories up to any fixed time, a phenomenon we refer to as “propagation of ergodicity”. Along the way, we develop some general results on local weak convergence of Gibbs measures in the uniqueness regime which appear to be new.
具有动态变化的多色边缘的随机图上的平均场相互作用
影响因子：
1.4
作者：
Bayraktar, Erhan;Wu, Ruoyu
通讯作者：
Wu, Ruoyu