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Communications in Mathematical Physics

, Volume 291, Issue 1, pp 177–224 | Cite as

The Ginibre Ensemble of Real Random Matrices and its Scaling Limits

  • A. Borodin
  • C. D. SinclairEmail author
Article

Abstract

We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a 2 × 2 matrix kernel associated to the ensemble. We apply this result to the real Ginibre ensemble and compute the bulk and edge scaling limits of its correlation functions as the size of the matrices becomes large.

Keywords

Correlation Function Point Process Random Matrix Matrix Kernel Scaling Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Mathematics 253-37California Institute of TechnologyPasadenaUSA
  2. 2.Department of MathematicsUniversity of ColoradoBoulderUSA

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