A note on pair-dependent linear statistics with a slowly increasing variance

@article{Aguirre2020ANO,
  title={A note on pair-dependent linear statistics with a slowly increasing variance},
  author={Ander Aguirre and A. Soshnikov},
  journal={arXiv: Probability},
  year={2020}
}
We prove Gaussian fluctuation for pair counting statistics of the form $ \sum_{1\leq i\neq j\leq N} f(\theta_i-\theta_j)$ for the Circular Unitary Ensemble (CUE) of random matrices in the case of a slowly growing variance in the limit of large $N.$ 

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