3 papers
math-ph2009★ 32 cited
Topological expansion of the Bethe ansatz, and quantum algebraic geometry
L. Chekhov, B. Eynard, O. Marchal
In this article, we solve the loop equations of the β-random matrix model, in a way similar to what was found for the case of hermitian matrices β=1. For β=1, the solution was expr…
math-ph2008★ 44 cited
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…
nlin.SI2008★ 18 cited
The partition function of the two-matrix model as an isomonodromic tau-function
M. Bertola, O. Marchal
We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that the partition function is an isomonodromic tau function in a sense that generalizes Jimbo-Miwa-Ueno's. I…