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Loop Models, Random Matrices and Planar Algebras

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Abstract

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.

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Authors and Affiliations

  1. UMPA, CNRS UMR 5669, ENS Lyon, 46 allée d’Italie, 69007, Lyon, France

    A. Guionnet

  2. Department of Mathematics, UC Berkeley, Berkeley, CA, 94720, USA

    V. F. R. Jones

  3. Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA

    D. Shlyakhtenko

  4. UPMC Univ Paris 6, CNRS UMR 7589, LPTHE, 75252, Paris Cedex, France

    P. Zinn-Justin

Authors
  1. A. Guionnet
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  2. V. F. R. Jones
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  3. D. Shlyakhtenko
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  4. P. Zinn-Justin
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Correspondence to A. Guionnet.

Additional information

Communicated by H.-T. Yau

A.G. and P.Z.-J. are supported by the ANR project ANR-08-BLAN-0311-01.

V.J.’s research is supported by NSF grant DMS-0856316.

D.S.’s research is supported by NSF grant DMS-0900776.

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Guionnet, A., Jones, V.F.R., Shlyakhtenko, D. et al. Loop Models, Random Matrices and Planar Algebras. Commun. Math. Phys. 316, 45–97 (2012). https://doi.org/10.1007/s00220-012-1573-1

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  • DOI: https://doi.org/10.1007/s00220-012-1573-1

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