# 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)