A factorization of determinant related to some random matrices

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Abstract

We consider the expectation of the determinant del(λ - X)-1 for Im λ > 0 associated with some random NxN matrices and factorize it into N Stieltjes transforms of probability measures. Moreover, using this factorization, we investigate the limiting behavior of the logarithm of the quantity as N → ∞.

Original languageEnglish
Pages (from-to)1449-1459
Number of pages11
JournalJournal of Statistical Physics
Volume90
Issue number5-6
Publication statusPublished - Mar 1 1998
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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