Simple matrix models for random Bergman metrics

Frank Ferrari*, Semyon Klevtsov, Steve Zelditch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Recently, the authors have proposed a new approach to the theory of random metrics, making an explicit link between probability measures on the space of metrics on a Kähler manifold and random matrix models. We consider simple examples of such models and study the one-and two-point functions of the metric. These geometric correlation functions correspond to new interesting types of matrix model correlators. We provide in particular a detailed study of the Wishart model, where we determine the correlation functions explicitly. We find that the random measure in this model turns out to be concentrated on the background metric in the large N limit.

Original languageEnglish (US)
Article numberP04012
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2012
Issue number4
DOIs
StatePublished - Apr 2012

Keywords

  • correlation functions
  • matrix models
  • random lattices (surfaces)

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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