39 citations · 157 across the 12 of their papers we have counts for
13 papers
Counting mobiles by integrable systems
Michel Bergère, Bertrand Eynard, Emmanuel Guitter +1
Mobiles are a particular class of decorated plane trees which serve as codings for planar maps. Here we address the question of enumerating mobiles in their most general flavor, in…
Rational differential systems, loop equations, and application to the q-th reductions of KP
Michel Bergère, Gaëtan Borot, Bertrand Eynard
To any solution of a linear system of differential equations, we associate a kernel, correlators satisfying a set of loop equations, and in presence of isomonodromic parameters, a…
The sine-law gap probability, Painlevé 5, and asymptotic expansion by the topological recursion
Olivier Marchal, Bertrand Eynard, Michel Bergère
The goal of this article is to rederive the connection between the Painlevé integrable system and the universal eigenvalues correlation functions of double-scaled hermitian mat…
Loop equations and topological recursion for the arbitrary- two-matrix model
Michel Bergère, Bertrand Eynard, Olivier Marchal +1
We write the loop equations for the two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leadi…
Universal scaling limits of matrix models, and (p,q) Liouville gravity
Michel Bergere, Bertrand Eynard
We show that near a point where the equilibrium density of eigenvalues of a matrix model behaves like y ~ x^{p/q}, the correlation functions of a random matrix, are, to leading ord…
Determinantal formulae and loop equations
Michel Bergère, Bertrand Eynard
We prove that the correlations functions, generated by the determinantal process of the Christoffel-Darboux kernel of an arbitrary order 2 ODE, do satisfy loop equations.