Title: Fractal Gaussian networks: A sparse random graph model based on gaussian multiplicative chaos
Authors: Krishnakumar Balasubramanian - University of California, Davis (United States) [presenting]
Abstract: A novel stochastic network model is introduced, which is 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. They 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 edge/triangle counts, spectral properties) and statistical question (e.g, detecting the presence of fractality and parameter estimation based on observed network data) related to FGNs.