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## Abstract

Using a Coulomb gas approach, we compute the generating function of the covariances of power traces for one-cut β-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 β-ensemble. As particular cases of the main result we consider the classical β-Gaussian, β-Wishart and β-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.

Original language | English |
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Article number | 315204 |

Number of pages | 23 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 31 |

DOIs | |

Publication status | Published - 20 Jul 2015 |

## Keywords

- matrix models
- 2D Coulomb gas
- correlated random variables

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