Clt for Fluctuations of Β-ensembles with General Potential

  title={Clt for Fluctuations of Β-ensembles with General Potential},
  author={THOMAS LEBL{\'E} and Sylvia Serfaty},
We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or β-ensembles. We use a method based on a change of variables which allows to treat fairly general situations, including multi-cut and, for the first time, critical cases, and generalizes the previously known results of Johansson, Borot-Guionnet and Shcherbina. In the one-cut regular case, our approach also allows to retrieve a rate of convergence as well as previously known expansions of the free energy… CONTINUE READING

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