Geodesic
A~note on pair-dependent linear statistics with a~slowly increasing variance
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 502-512

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We prove Gaussian fluctuations for pair-counting statistics of the form $\Sigma_{1\le i\ne j\le N}f(\theta_i-\theta_j)$ for the circular unitary ensemble of random matrices in the large-$N$ limit under the condition that the variance increases slowly as $N$ increases.
Mots-clés : random matrix
Keywords: circular unitary ensemble, pair-counting statistics, central limit theorem. 
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     author = {A. Aguirre and A. B. Soshnikov},
     title = {A~note on pair-dependent linear statistics with a~slowly increasing variance},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {502--512},
     publisher = {mathdoc},
     volume = {205},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a8/}
}
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A. Aguirre; A. B. Soshnikov. A~note on pair-dependent linear statistics with a~slowly increasing variance. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 502-512. http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a8/