Communications in Mathematical Physics

, Volume 316, Issue 1, pp 45–97

Loop Models, Random Matrices and Planar Algebras

  • A. Guionnet
  • V. F. R. Jones
  • D. Shlyakhtenko
  • P. Zinn-Justin

DOI: 10.1007/s00220-012-1573-1

Cite this article as:
Guionnet, A., Jones, V.F.R., Shlyakhtenko, D. et al. Commun. Math. Phys. (2012) 316: 45. doi:10.1007/s00220-012-1573-1


We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar algebra. We apply this construction to compute the generating functions of the Potts model on a random planar map.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • A. Guionnet
    • 1
  • V. F. R. Jones
    • 2
  • D. Shlyakhtenko
    • 3
  • P. Zinn-Justin
    • 4
  1. 1.UMPA, CNRS UMR 5669, ENS LyonLyonFrance
  2. 2.Department of MathematicsUC BerkeleyBerkeleyUSA
  3. 3.Department of MathematicsUCLALos AngelesUSA
  4. 4.UPMC Univ Paris 6, CNRS UMR 7589, LPTHEParis CedexFrance

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