Higher-order fluctuations in dense random graph models
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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. The main motivation to investigate these statistics is the fact that they are key to understanding fluctuations of regular subgraph counts – the cornerstone of dense graph limit theory – since they act as an orthogonal basis of a corresponding L_2 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. With this article, we believe we answer the question "What is the central limit theorem of dense graph limit theory?".
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