论文标题
密集的随机图模型中的高阶波动
Higher-order fluctuations in dense random graph models
论文作者
论文摘要
我们的主要结果是在由一般图形和独立顶点标签产生的随机图中的中心子图计数的多元正常近似中的定量界限。我们对这些统计数据很感兴趣，因为它们是理解常规子图计数波动的关键 - 密集图极限理论的基石。我们还通过广义$ U $统计和高斯希尔伯特空间的理论来确定所得的限制高斯随机度量，我们认为这是一个合适的框架，可以在密集的随机图模型中描述和理解高阶波动。在本文中，我们相信我们回答了一个问题：“密集图极限理论的中心限制定理是什么？”。我们将理论与一些统计应用相辅相成，以说明在网络建模中使用中心子图计数的使用。
Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts in random graphs generated by a general graphon and independent vertex labels. We are interested in these statistics because they are key to understanding fluctuations of regular subgraph counts -- a cornerstone of dense graph limit theory. We also identify the resulting limiting Gaussian stochastic measures by means of the theory of generalised $U$-statistics and Gaussian Hilbert spaces, which we think is a suitable framework to describe and understand higher-order fluctuations in dense random graph models. With this article, we believe we answer the question "What is the central limit theorem of dense graph limit theory?". We complement the theory with some statistical applications to illustrate the use of centred subgraph counts in network modelling.
