Central Limit Theorem for CβE Pair Dependent Statistics in Mesoscopic Regime

2021/09/27 by Aguirre, Ander, Soshnikov, Alexander
#60B20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2109.13339

Abstract

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

Related

• Mesoscopic central limit theorem for the circular beta-ensembles and applications
• Pair Dependent Linear Statistics for Circular Beta Ensemble
• Mesoscopic central limit theorem for general β-ensembles
• Mesoscopic Universality for Circular Orthogonal Polynomial Ensembles
• Gaussian fluctuations for βEnsembles