Loop models, random matrices and planar algebras

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.

References in corpus (3)

• Random matrices, free probability, planar algebras and subfactors
• Combinatorial aspects of matrix models
• An orthogonal approach to the subfactor of a planar algebra

Cited by in corpus (16)

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• Free transport for interpolated free group factors
• Sandpiles and unicycles on random planar maps
• Free analysis and planar algebras
• Motzkin Algebras and the $A_n$ Tensor Categories of Bimodules
• Free transport for finite depth subfactor planar algebras
• On the symmetric enveloping algebra of planar algebra subfactors
• A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions
• Random Matrices, Boundaries and Branes
• Sums of Random Matrices and the Potts Model on Random Planar Maps