Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos
In this talk, I will introduce a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right from probability theory. FGNs interpolate continuously between the popular purely random geometric graphs (aka the Poisson Boolean network), and random graphs with increasingly fractal behavior. After introducing and motivating the model, I will discuss some probabilistic (e.g., expected motif counts, spectral properties) and statistical question (e.g., detecting the presence of fractality and parameter estimation based on observed network data) related to FGNs, and present some preliminary real-world network data analysis.