  The problem of non--interacting electrons on a square lattice subject to a
random magnetic flux is mapped onto a one--dimensional model with infinitely
many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps
the problem onto Wegner's $N$-orbital model in the same limit, while the
original problem corresponds to $N=1$. The exact solution for $N=\infty$, the
mean--field limit, is discussed and compared with numerical results. An outline
of a $1/N$-expansion is given.
