Mixed correlation functions in the 2-matrix model
and the Bethe ansatz

Nicolas Orantin

Abstract:

Considering that the mean value of a trace of a product of random matrices is the generating function of
discretised surfaces with one boundary, the mixed correlation functions of the 2-matrix model generate all
possible boundary conditions. As an example: <Tr (M_1^k M_2^l M_1^k' M_2^l' M_1^k'' M_2^l''> generates
the surfaces with one boundary made of k conditions 1 followed by l conditions 2, k' conditions 1, l' conditions 2,
k'' conditions 1 and l'' conditions 1. We have been able to compute explicitly all the mixed traces using a formula
similar to a Bethe Ansatz.

(Joint work withwith Bertrand Eynard)