Asymptotic analysis of random matrices with external source and a family of algebraic curves

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Abstract

We present a set of conditions which, if satisfied, provide for a complete asymptotic analysis of random matrices with a source term containing two distinct eigenvalues. These conditions are shown to be equivalent to the existence of a particular algebraic curve. For the case of a quartic external field, the curve in question is proven to exist, yielding precise asymptotic information about the limiting mean density of eigenvalues, as well as bulk and edge universality.

Original languageEnglish (US)
Article number002
Pages (from-to)1547-1571
Number of pages25
JournalNonlinearity
Volume20
Issue number7
DOIs
Publication statusPublished - Jul 1 2007

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

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