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Central Limit Theorem for $CβE$ Pair Dependent Statistics in Mesoscopic Regime
Ander Aguirre, Alexander Soshnikov · 2021-09-28 · via math.PR updates on arXiv.org

We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble $\sum_{i\neq j}f(L_N(θ_i-θ_j))$ for arbitrary $β>0$ in the mesoscopic regime $L_N=O(N^{2/3-ε})$.

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