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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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