%0 Journal Article
%T A unified fluctuation formula for one-cut $¦Â$-ensembles of random matrices
%A Fabio Deelan Cunden
%A Francesco Mezzadri
%A Pierpaolo Vivo
%J Mathematics
%D 2015
%I arXiv
%R 10.1088/1751-8113/48/31/315204
%X Using a Coulomb gas approach, we compute the generating function of the covariances of power traces for one-cut $\beta$-ensembles of random matrices in the limit of large matrix size. This formula depends only on the support of the spectral density, and is therefore universal for a large class of models. This allows us to derive a closed-form expression for the limiting covariances of an arbitrary one-cut $\beta$-ensemble. As particular cases of the main result we consider the classical $\beta$-Gaussian, $\beta$-Wishart and $\beta$-Jacobi ensembles, for which we derive previously available results as well as new ones within a unified simple framework. We also discuss the connections between the problem of trace fluctuations for the Gaussian Unitary Ensemble and the enumeration of planar maps.
%U http://arxiv.org/abs/1504.03526v2