A shortcut through the Coulomb gas method for spectral linear statistics on random matrices

Fabio Deelan Cunden, Paolo Facchi, Pierpaolo Vivo

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

17 Citations (Scopus)
3985 Downloads (Pure)

Abstract

In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two-dimensional Coulomb gas analogy is available. We present a critical revision of the Coulomb gas method in random matrix theory (RMT) borrowing language and tools from large deviations theory. This allows us to formalize an equivalent, but more effective and quicker route toward RMT free energy calculations. Moreover, we argue that this more modern viewpoint is likely to shed further light on the interesting issues
Original languageEnglish
Article number135202
Number of pages19
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number13
Early online date17 Feb 2016
DOIs
Publication statusPublished - 1 Apr 2016

Keywords

  • random matrix theory
  • 2D Coulomb gas
  • large deviations
  • phase transitions

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