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- W4316830063 abstract "We establish a central limit theorem for the fluctuations of the empirical measure in the $beta$-ensemble of dimension $N$ at a temperature proportional to $N$ and with confining smooth potential. The space of test functions for which the CLT holds includes $mathcal{C}^1$, vanishing functions at infinity. It is obtained by the inversion of an operator which is a pertubation of a Sturm-Liouville operator. The method that we use is based on a change of variables introduced by Bekerman, Guionnet and Figalli in arXiv:1311.2315 and by Shcherbina in arXiv:1310.7835." @default.
- W4316830063 created "2023-01-17" @default.
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- W4316830063 date "2023-01-13" @default.
- W4316830063 modified "2023-09-27" @default.
- W4316830063 title "CLT for real $beta$-ensembles at high temperature" @default.
- W4316830063 doi "https://doi.org/10.48550/arxiv.2301.05516" @default.
- W4316830063 hasPublicationYear "2023" @default.
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