Communications in Mathematical Physics

, Volume 316, Issue 1, pp 45-97

First online:

Loop Models, Random Matrices and Planar Algebras

  • A. GuionnetAffiliated withUMPA, CNRS UMR 5669, ENS Lyon Email author 
  • , V. F. R. JonesAffiliated withDepartment of Mathematics, UC Berkeley
  • , D. ShlyakhtenkoAffiliated withDepartment of Mathematics, UCLA
  • , P. Zinn-JustinAffiliated withUPMC Univ Paris 6, CNRS UMR 7589, LPTHE

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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.