Detection thresholds for random geometric graphs

Random geometric graphs hide geometric structure inside an otherwise random-looking network: each vertex has a latent position on a high-dimensional sphere, and edges are formed between vertices that are sufficiently close. When can this hidden geometry be detected from the graph alone? In this talk, I will discuss recent results establishing indistinguishability from Erdős–Rényi random graphs above the conjectured sharp dimension threshold, whenever the average degree grows polynomially with the number of vertices.

This talk is based on joint work with Cheng Mao (Georgia Tech), Nike Sun (MIT), Yihong Wu (Yale), and Jialing Xu (Duke).