Title: Higher-Order Graphon Theory: Fluctuations and Degeneracies
Speaker: Bhaswar Bhattacharya (University of Pennsylvania / Wharton School, Philadelphia, USA)
Date: 16 November 2022
Time: 2:30 pm
Venue: LH-1, Mathematics Department
Motifs (patterns of subgraphs), such as edges and triangles, encode important structural information
about the geometry of a network and are the central objects in graph limit (graphon) theory. In this
talk we will derive the higher-order fluctuations (asymptotic distributions) of subgraph counts in
an inhomogeneous random graph sampled from a graphon. We will show that the limiting distributions
of subgraph counts can have both Gaussian or non-Gaussian components, depending on a notion of
regularity of subgraphs, where the non-Gaussian component is an infinite weighted sum of centered
chi-squared random variables with the weights determined by the spectral properties of the graphon.
We will also discuss various structure theorems and open questions about degeneracies of the limiting
distribution and connections to quasirandom graphs.
(Joint work with Anirban Chatterjee and Svante Janson.)