Reduction of internal degrees of freedom in the large N limit in matrix models

Abstract

In this paper the large $N$ limit of one hermitian matrix models coupled to an external matrix is considered. It is shown that in the large N limit the number of degrees of freedom are reduced to be order N even though it is order $N^{2}$ for finite N. It is claimed that this result is the origin of the factorization of observables in the path integral formalism.