Abstract

In this talk, I will present the multivariate normal approximation for the centered subgraph counts in dense random graphs. The main motivation to investigate these statistics is the fact that they are key to understanding fluctuations of regular subgraph counts since they act as an orthogonal basis of a corresponding L2 space. 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.
This is joint work with Adrian Roellin.