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The Ginibre Ensemble of Real Random Matrices and its Scaling Limits

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An Erratum to this article was published on 27 July 2016

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.

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Authors and Affiliations

  1. Mathematics 253-37, California Institute of Technology, Pasadena, California, 91125, USA

    A. Borodin

  2. Department of Mathematics, University of Colorado, Boulder, Colorado, 80309, USA

    C. D. Sinclair

Authors
  1. A. Borodin
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  2. C. D. Sinclair
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Correspondence to C. D. Sinclair.

Additional information

Communicated by S. Zelditch

An erratum to this article is available at http://dx.doi.org/10.1007/s00220-016-2703-y.

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Borodin, A., Sinclair, C.D. The Ginibre Ensemble of Real Random Matrices and its Scaling Limits. Commun. Math. Phys. 291, 177–224 (2009). https://doi.org/10.1007/s00220-009-0874-5

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  • DOI: https://doi.org/10.1007/s00220-009-0874-5

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