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Updated: Jan 17, 2026

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Published on: September 25, 2021
Weak-Correlation Universality and Macroscopic Fluctuations in Power-Law Recurrent Networks
1Humboldt-Universität zu Berlin, Institute for Theoretical Biology, Department of Biology, 10115 Berlin, Germany.
None:
Balanced network theory describes the dynamic state of randomly connected systems with intrinsic negative feedback, predicting the suppression of correlations as connectivity increases. We show that this weak-correlation universality holds broadly but breaks down in power-law networks where the largest out-degrees scale with system size. In such networks, residual correlations cross over to a regime that retains macroscopic fluctuations in the thermodynamic limit. Unlike Erdös-Rényi networks, the degree heterogeneity of power-law topologies amplifies coherent population-level fluctuations. Our results provide a theoretical foundation for the strong correlations observed in real-world networks with sparse and heterogeneous connectivity.
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