Abstract:Année de publication : 2010
We study integrals over Hermitian supermatrices of arbitrary size $p+q$, that are parametrized by an external field $X$ and a source $Y$, of respective size $m+n$ and $p+q$. We show that these integrals exhibit a simple topological expansions in powers of $(p-q)^2$. The loop equation and the associated spectral curve are also obtained. The solutions to the loop equation are given in terms of the symplectic invariants introduced \cite{EOFg}. The symmetry property of the latter objects allows us to prove a duality that relates supermatrix models in which the role of $X$ and $Y$ are interchanged.