Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions

@article{Torquato2021LocalNF,
  title={Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions},
  author={Salvatore Torquato and Jaeuk Kim and Michael Andreas Klatt},
  journal={Physical Review X},
  year={2021},
  volume={11}
}
The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To better characterize density fluctuations, we carry out an extensive study of higher-order moments, including the skewness $\gamma_1(R)$, excess kurtosis $\gamma_2(R)$ and… 

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