Bian Zheng, Lamb Jeroen S W, Pereira Tiago
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 13566-590 São Carlos, Brazil.
Department of Mathematics, Imperial College London, SW7 2AZ London, UK.
Commun Math Phys. 2025;406(7):170. doi: 10.1007/s00220-025-05335-0. Epub 2025 Jun 23.
We study a class of heterogeneous random networks, where the network degree distribution follows a power-law, and each node dynamics is a random dynamical system, interacting with neighboring nodes via a random coupling function. We characterize the hub behavior by the mean-field, subject to statistically controlled fluctuations. In particular, we prove that the fluctuations are 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, namely, a scaling relation between system size and frequency of large fluctuations, the system size induced desynchronization, and the Gaussian behavior of the fluctuations.
我们研究一类异构随机网络，其中网络度分布遵循幂律，并且每个节点动力学是一个随机动力系统，通过随机耦合函数与相邻节点相互作用。我们通过平均场来刻画中心节点行为，并考虑统计控制下的涨落。特别地，我们证明了在指数长时间尺度上涨落很小，并得到了任意固定时刻涨落统计量的贝里 - 埃森估计。我们的结果为几个数值观测结果提供了解释，即系统大小与大幅涨落频率之间的标度关系、系统大小引起的去同步化以及涨落的高斯行为。
