Corpus ID: 209376555

Pair Dependent Linear Statistics for Circular Beta Ensemble

@article{Aguirre2019PairDL,
  title={Pair Dependent Linear Statistics for Circular Beta Ensemble},
  author={Ander Aguirre and A. Soshnikov and Joshua Sumpter},
  journal={arXiv: Probability},
  year={2019}
}
We study limiting distribution of pair counting statistics of the form $ \sum_{1\leq i\neq j\leq N} f(L_N\*(\theta_i-\theta_j))$ for the circular $\beta$-ensemble (C$\beta$E) of random matrices for sufficiently smooth test function $f$ and $L_N=O(N).$ For $\beta=2$ and $L_N=N$ our results are inspired by a classical result of Montgomery on pair correlation of zeros of Riemann zeta function. 
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