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CLT for fluctuations of $\beta$-ensembles with general potential. (arXiv:1706.09663v1 [math-ph])
来源于:arXiv
We prove a central limit theorem for the linear statistics of one-dimensional
log-gases, or $\beta$-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 to arbitrary order. 查看全文>>