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Central limit theorem for \(C\beta E\) pair dependent statistics in mesoscopic regime. (English) Zbl 07592528

Summary: We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble \(\sum_{i\ne j} f(L_N(\theta_i-\theta_j))\) for arbitrary \(\beta > 0\) in the mesoscopic regime \(L_N=\mathcal{O}(N^{2/ 3-\epsilon})\). In addition, we obtain similar results for bipartite statistics.

MSC:

62-XX Statistics
60F05 Central limit and other weak theorems
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