Guarantees for Spontaneous Synchronization on Random Geometric Graphs

Pedro Abdalla, Afonso S. Bandeira, Clara Invernizzi

Published 2022-08-25Version 1

The Kuramoto model is an important mathematical model to study the synchronization phenomena in complex networks. The rich theory behind the rigorous treatment of the synchronization phenomenon has been connected to many branches of science. In particular, the study of the energy function associated with the Kuramoto model is relevant in the context of non-convex optimization for machine learning and data science. In this work, we use tools from random matrix theory, random graphs, and statistics to derive rigorous guarantees for the random geometric graph on the sphere to synchronize with probability of success tending to one as the number of nodes tends to infinity. To the best of our knowledge, this is the first rigorous result for the Kuramoto model on random geometric graphs.