论文标题
全球和局部经验弥散图的中心限制定理
Central Limit Theorems for global and local empirical measures of diffusions on Erdős-Rényi graphs
论文作者
论文摘要
我们解决了在可能稀释的Erdős-rényi图上相互作用的（局部和全局）扩散的（局部和全局）经验度量的中心限制定理的问题。特别注意初始条件（不一定是I.I.D.）对限制波动性质的影响。我们特别证明，当从图中独立选择初始条件时，波动保持与平均场框架相同。我们给出了一个依靠图表的精心选择的初始数据的非普遍波动的示例。证明的关键工具是使用Grothendieck不平等的扩展。
We address the issue of the Central Limit Theorem for (both local and global) empirical measures of diffusions interacting on a possibly diluted Erdős-Rényi graph. Special attention is given to the influence of initial condition (not necessarily i.i.d.) on the nature of the limiting fluctuations. We prove in particular that the fluctuations remain the same as in the mean-field framework when the initial condition is chosen independently from the graph. We give an example of non-universal fluctuations for carefully chosen initial data that depends on the graph. A crucial tool for the proof is the use of extensions of Grothendieck inequality.
