Non-hermitian random matrix models

Romuald A. Janik, Maciej A. Nowak, Gábor Papp, Ismail Zahed

Research output: Contribution to journalArticle

80 Citations (Scopus)

Abstract

We introduce an extension of the diagrammatic rules in random matrix theory and apply it to non-hermitian random matrix models using the 1/N approximation. A number of one-and two-point functions are evaluated on their holomorphic and non-holomorphic supports to leading order in 1/N. The one-point functions describe the distribution of eigenvalues, while the two-point functions characterize their macroscopic correlations. The generic form for the two-point functions is obtained, generalizing the concept of macroscopic universality to non-hermitian random matrices. We show that the holomorphic and non-holomorphic one-and two-point functions condition the behavior of pertinent partition functions to order script O sign(1/N). We derive explicit conditions for the location and distribution of their singularities. Most of our analytical results are found to be in good agreement with numerical calculations using large ensembles of complex matrices.

Original languageEnglish
Pages (from-to)603-642
Number of pages40
JournalNuclear Physics B
Volume501
Issue number3
DOIs
Publication statusPublished - Sep 22 1997

Keywords

  • Diagrammatic expansion
  • Non-hermitian random matrix models
  • Universal correlator

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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