# A local CLT for linear statistics of 2D Coulomb gases

@article{Leble2020ALC, title={A local CLT for linear statistics of 2D Coulomb gases}, author={Thomas Lebl'e and Ofer Zeitouni}, journal={arXiv: Probability}, year={2020} }

We prove a local central limit theorem for fluctuations of linear statistics of smooth enough test functions under the canonical Gibbs measure of two-dimensional Coulomb gases at any positive temperature. The proof relies on the existing global central limit theorem and a new decay estimate for the characteristic function of such fluctuations.

## 3 Citations

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