A local CLT for linear statistics of 2D Coulomb gases
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2020
- DOI:
- 10.48550/arXiv.2005.12163
- arXiv:
- arXiv:2005.12163
- Bibcode:
- 2020arXiv200512163L
- Keywords:
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- Mathematics - Probability;
- Mathematical Physics
- E-Print:
- 15p Final version, to appear in Markov Processes and Related Fields