Journal of Statistical Physics

, Volume 90, Issue 5–6, pp 1449–1459 | Cite as

A Factorization of Determinant Related to Some Random Matrices

  • Tomoyuki Shirai
Article

Abstract

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

Scattering problem random matrix (GUE) factorization orthogonal polynomials semicircle law 

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Tomoyuki Shirai
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversitySakyo-ku, KyotoJapan

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