标题： 非确定性相互作用粒子在稀疏随机图上的大偏差 显示英文标题

标题： Large Deviations of Non-Stochastic Interacting Particles on Sparse Random Graphs

摘要： 本文研究了随机图上相互作用粒子系统的大偏差。 没有随机性，唯一的无序来源是随机图的连接和初始条件。 任何特定顶点上的传入边的平均数量必须随着$N\to \infty$发散到无穷大，但可以以任意缓慢的速度发散。 因此，这些结果适用于稀疏和密集的随机图。 提供了一个对稀疏 Erdos-Renyi 图的特定应用。 定理是通过将由初始条件生成的“嵌套经验测度”的大偏差原理推进到动力学中来证明的。 嵌套经验测度可以看作是边连接密度的密度：相关的弱拓扑比由图切割范数生成的拓扑更粗糙，因此应用范围更广。 显示英文摘要

摘要： 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.