论文标题
稀疏随机图上的非较大相互作用粒子的大偏差
Large Deviations of Non-Stochastic Interacting Particles on Sparse Random Graphs
论文作者
论文摘要
本文涉及随机图上相互作用粒子系统的巨大偏差。没有随机性，唯一的疾病来源是随机图连接和初始条件。任何特定顶点的传入边缘的平均传入边缘必须以$ n \ to \ infty $的形式分歧，但可以以任意缓慢的速度这样做。因此，对于稀疏和密集的随机图，这些结果都是准确的。提供了稀疏的Erdos-Renyi图的特定应用。通过推动最初条件到动力学产生的“嵌套经验度量”的大偏差原理来证明该定理。可以将嵌套的经验度量视为边缘连接密度的密度：相关的弱拓扑比绘制剪切规范产生的拓扑更粗糙，因此应用范围更广泛。
This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of afferent edges on any particular vertex must diverge to infinity as $N\to \infty$, but can do so at an arbitrarily slow rate. These results are thus accurate for both sparse and dense random graphs. A particular application to sparse Erdos-Renyi graphs is provided. The theorem is proved by pushing forward a Large Deviation Principle for a `nested empirical measure' generated by the initial conditions to the dynamics. The nested empirical measure can be thought of as the density of the density of edge connections: the associated weak topology is more coarse than the topology generated by the graph cut norm, and thus there is a broader range of application.
