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arXiv · 1912.07110

Pair Dependent Linear Statistics for Circular Beta Ensemble

Ander Aguirre·Alexander Soshnikov·Joshua Sumpter
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Abstract

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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Ander Aguirre, Alexander Soshnikov, Joshua Sumpter. 2019-12-15. Pair Dependent Linear Statistics for Circular Beta Ensemble. https://arxiv.org/abs/1912.07110

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