Complex versus hermitian matrix models:an explicit calculation of integralsover the unitary ensembleas gaussian triangular integrals
We prove that the complex matrix model and 2-hermitian matrix model obey the same loop equations. By representing both matrix integrals in terms of eigenvalues integrals, we obtain that integrals over the unitary group (of Shatashvili’s form) can be written as gaussian integrals over the set of triangular matrices. And the later triangular integrals are computed very explicitly.
Université de Barcelone
