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

Fabio Cunden, Francesco Mezzadri, Pierpaolo Vivo

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)
228 Downloads (Pure)

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 languageEnglish
Article number315204
Number of pages23
JournalJournal of Physics A: Mathematical and Theoretical
Volume48
Issue number31
DOIs
Publication statusPublished - 20 Jul 2015

Keywords

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

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