NeuroMat Seminar - Mean-Field and Fluctuations for Hub Dynamics in Heterogeneous Random Networks

Mar 25, 2026

We study a class of heterogeneous random networks where the degree distribution follows a power law and each node's dynamics is governed by a random dynamical system interacting with neighboring nodes via a random coupling function. We characterize hub behavior through the mean-field, subject to statistically controlled fluctuations. In particular, we prove that fluctuations remain small over exponentially long time scales and obtain Berry–Esseen estimates for the fluctuation statistics at any fixed time. Our results provide an explanation for several numerical observations: a scaling relation between system size and the frequency of large fluctuations, system-size-induced desynchronization, and the Gaussian behavior of the fluctuations.