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A note on pair dependent linear statistics with slowly growing variance

Probability 2021-02-03 v1 Mathematical Physics math.MP

Abstract

We prove Gaussian fluctuation for pair counting statistics of the form 1ijNf(θiθj) \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.N.

Keywords

Cite

@article{arxiv.2004.01345,
  title  = {A note on pair dependent linear statistics with slowly growing variance},
  author = {Ander Aguirre and Alexander Soshnikov},
  journal= {arXiv preprint arXiv:2004.01345},
  year   = {2021}
}
R2 v1 2026-06-23T14:37:38.202Z