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6 papers · 2 filters
Statistics of geodesics in large quadrangulations
J. Bouttier, E. Guitter
We study the statistical properties of geodesics, i.e. paths of minimal length, in large random planar quadrangulations. We extend Schaeffer's well-labeled tree bijection to the ca…
Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
P. Di Francesco, P. Zinn-Justin
We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation with reflecting boundary conditions which is relevant to the Temperley--Lieb model of loops on a strip.…
Combinatorial aspects of boundary loop models
Jesper Lykke Jacobsen, Hubert Saleur
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they…
Quantum decay rates in chaotic scattering
Stephane Nonnenmacher, Maciej Zworski
In this article we prove that for a large class of operators, including Schroedinger operators, with hyperbolic classical flows, the smallness of dimension of the trapped set impli…
Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models
Bertrand Eynard, Nicolas Orantin
We show that Mirzakhani's recursions for the volumes of moduli space of Riemann surfaces are a special case of random matrix loop equations, and therefore we confirm again that Kon…
Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants
Bertrand Eynard, Nicolas Orantin
We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. generating function for counting bicolored discrete surfaces with non uniform bou…