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13 papers · 2 filters
Conformal two-boundary loop model on the annulus
Jerome Dubail, Jesper Lykke Jacobsen, Hubert Saleur
We study the two-boundary extension of a loop model - corresponding to the dense phase of the O(n) model, or to the Q=n^2 state Potts model - in the critical regime -2 < n < 2. Thi…
Algebraic methods in random matrices and enumerative geometry
Bertrand Eynard, Nicolas Orantin
We review the method of symplectic invariants recently introduced to solve matrix models loop equations, and further extended beyond the context of matrix models. For any given spe…
Weyl laws for partially open quantum maps
Emmanuel Schenck
We study a toy model for "partially open" wave-mechanical system, like for instance a dielectric micro-cavity, in the semiclassical limit where ray dynamics is applicable. Our mode…
Confluence of geodesic paths and separating loops in large planar quadrangulations
J. Bouttier, E. Guitter
We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minima…
Another derivation of the geometrical KPZ relations
Francois David, Michel Bauer
We give a physicist's derivation of the geometrical (in the spirit of Duplantier-Sheffield) KPZ relations, via heat kernel methods. It gives a covariant way to define neighborhoods…
Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry
Bertrand Eynard, Olivier Marchal
In this article, we define a non-commutative deformation of the "symplectic invariants" of an algebraic hyperelliptical plane curve. The necessary condition for our definition to m…