Central limit theorem for CβE pair dependent statistics in mesoscopic regime

Ander Aguirre; Alexander Soshnikov

doi:10.1214/22-ECP481

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Home > Journals > Electron. Commun. Probab. > Volume 27 > Article

2022 Central limit theorem for

C\beta E

pair dependent statistics in mesoscopic regime

Ander Aguirre, Alexander Soshnikov

Author Affiliations +

Ander Aguirre,¹ Alexander Soshnikov¹
¹University of California at Davis, United States of America

Electron. Commun. Probab. 27: 1-10 (2022). DOI: 10.1214/22-ECP481

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Abstract

We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble ${\textstyle\sum _{i\ne j}}f({L_{N}}({\theta _{i}}-{\theta _{j}}))$ for arbitrary $\beta \textgreater 0$ in the mesoscopic regime ${L_{N}}=\mathcal{O}({N^{2/ 3-\epsilon }})$ . In addition, we obtain similar results for bipartite statistics.

Funding Statement

Research has been partially supported by the Simons Foundation Collaboration Grant for Mathematicians #312391.

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Ander Aguirre. Alexander Soshnikov. "Central limit theorem for $C\beta E$ pair dependent statistics in mesoscopic regime." Electron. Commun. Probab. 27 1 - 10, 2022. https://doi.org/10.1214/22-ECP481