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

Guarantees for Spontaneous Synchronization on Random Geometric Graphs