Phase transitions in soft random geometric graphs

Stochastics Seminar
Thursday, January 13, 2022 - 3:30pm for 1 hour (actually 50 minutes)
Suqi Liu – Princeton University
Cheng Mao

Random graphs with latent geometric structure, where the edges are generated depending on some hidden random vectors, find broad applications in the real world, including social networks, wireless communications, and biological networks. As a first step to understand these models, the question of when they are different from random graphs with independent edges, i.e., Erd\H{o}s--R\'enyi graphs, has been studied recently. It was shown that geometry in these graphs is lost when the dimension of the latent space becomes large. In this talk, we focus on the case when there exist different notions of noise in the geometric graphs, and we show that there is a trade-off between dimensionality and noise in detecting geometry in the random graphs.