Central Limit Theorem for $C\beta E$ Pair Dependent Statistics in Mesoscopic Regime

Publication date: 27 September 2021

Abstract: We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble

s u m_{i e q j} f (L_{N} (h e t a_{i} - h e t a_{j}))

for arbitrary

in the mesoscopic regime

L_{N} = O (N^{2 / 3 - e p s i l o n})

.

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