A unified fluctuation formula for one-cut beta-ensembles of random matrices

作者：Cunden Fabio Deelan; Mezzadri Francesco; Vivo Pierpaolo

来源：Journal of Physics A-Mathematical and Theoretical, 2015, 48(31): 315204.

DOI：10.1088/1751-8113/48/31/315204

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

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.

• 出版日期2015-8-7