177 citations · 906 across the 50 of their papers we have counts for
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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…
Large-N asymptotic expansion for mean field models with Coulomb gas interaction
Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski
We derive the large-N, all order asymptotic expansion for a system of N particles with mean-field interactions on top of a Coulomb repulsion at temperature 1/β, under the assumptio…
Formal multidimensional integrals, stuffed maps, and topological recursion
Gaëtan Borot
We show that the large N expansion in the multi-trace 1 formal hermitian matrix model is governed by the topological recursion of [Eynard and Orantin, 2007] with initial conditions…
Abstract loop equations, topological recursion, and applications
Gaëtan Borot, Bertrand Eynard, Nicolas Orantin
We formulate a notion of abstract loop equations, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a unive…
Asymptotic expansion of beta matrix models in the multi-cut regime
Gaëtan Borot, Alice Guionnet
We establish the asymptotic expansion in matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segmen…