Matrix kernels for the Gaussian orthogonal and symplectic ensembles

Craig A. Tracy[1]; Harold Widom

  • [1] University of California, department of mathematics, Davis CA 95616 (USA), University of California, department of mathematics, Santa Cruz CA 95064 (USA)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 6, page 2197-2207
  • ISSN: 0373-0956

Abstract

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We derive the limiting matrix kernels for the Gaussian orthogonal and symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that ensure convergence of the determinants.

How to cite

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A. Tracy, Craig, and Widom, Harold. "Matrix kernels for the Gaussian orthogonal and symplectic ensembles." Annales de l’institut Fourier 55.6 (2005): 2197-2207. <http://eudml.org/doc/116250>.

@article{A2005,
abstract = {We derive the limiting matrix kernels for the Gaussian orthogonal and symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that ensure convergence of the determinants.},
affiliation = {University of California, department of mathematics, Davis CA 95616 (USA), University of California, department of mathematics, Santa Cruz CA 95064 (USA)},
author = {A. Tracy, Craig, Widom, Harold},
journal = {Annales de l’institut Fourier},
keywords = {random matrices; Gaussian orthogonal; symplectic ensembles},
language = {eng},
number = {6},
pages = {2197-2207},
publisher = {Association des Annales de l'Institut Fourier},
title = {Matrix kernels for the Gaussian orthogonal and symplectic ensembles},
url = {http://eudml.org/doc/116250},
volume = {55},
year = {2005},
}

TY - JOUR
AU - A. Tracy, Craig
AU - Widom, Harold
TI - Matrix kernels for the Gaussian orthogonal and symplectic ensembles
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 6
SP - 2197
EP - 2207
AB - We derive the limiting matrix kernels for the Gaussian orthogonal and symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that ensure convergence of the determinants.
LA - eng
KW - random matrices; Gaussian orthogonal; symplectic ensembles
UR - http://eudml.org/doc/116250
ER -

References

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  2. P.J. Forrester, T. Nagao, G. Honner, Correlations for the orthogonal-unitary and symplectic-unitary transitions at the soft and hard edges, Nucl. Phys. B 553 (1999), 601-643 Zbl0944.82012MR1707162
  3. J. Baik, E.M. Rains, Symmetrized random permutations, Random Matrix Models and Their Applications (2001), 1-19, Cambridge Univ. Press Zbl0989.60010
  4. I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, 35 (1969), Providence RI: Amer. Math. Soc. Zbl0181.13504MR246142
  5. K. Johansson, Toeplitz determinants, random growth and determinantal processes, Proc. of the International Congress of Mathematicians (2002), 53-52, Higher Education Press Zbl1001.60011
  6. M.L. Mehta, Random Matrices, (1991), London: Academic Press Zbl0780.60014MR1083764
  7. F.W.J. Olver, Asymptotics and Special Functions, (1974), New York: Academic Press Zbl0303.41035MR435697
  8. M. Prähofer, H. Spohn, Universal distributions for growth processes in 1 + 1 dimensions and random matrices, Phys. Rev. Letts. 84 (2000), 4882-4885 Zbl0976.82042
  9. C.A. Tracy, H. Widom, On orthogonal and symplectic matrix ensembles, Commun. Math. Phys. 177 (1996), 727-754 Zbl0851.60101MR1385083
  10. C.A. Tracy, H. Widom, Correlation functions, cluster functions and spacing distributions for random matrices, J. Stat. Phys. 92 (1998), 809-835 Zbl0942.60099MR1657844
  11. C.A. Tracy, H. Widom, Distribution functions for largest eigenvalues and their applications, I (2002), 587-596, Higher Education Press Zbl1033.82010

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