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Central Limit Theorem for $CβE$ Pair Dependent Statistics in Mesoscopic Regime (2109.13339v3)
Published 27 Sep 2021 in math.PR, math-ph, and math.MP
Abstract: We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble $\sum_{i\neq j}f(L_N(\theta_i-\theta_j))$ for arbitrary $\beta>0$ in the mesoscopic regime $L_N=O(N{2/3-\epsilon})$.
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