  The localization behavior of noninteracting two-dimensional electrons in a
random potential and strong magnetic field is of fundamental interest for the
physics of the quantum Hall effect. In order to understand the emergence of
power-law delocalization near the discrete extended-state energies $E_n = \hbar
\omega_c (n+{1/2})$, we study a generalization of the disorder-averaged
Liouvillian framework for the lowest Landau level to $N$ flavors of electron
densities (N=1 for the physical case). We find analytically the large-N limit
and 1/N corrections for all disorder strengths: at $N = \infty$ this gives an
estimate of the critical conductivity, and at order 1/N an estimate of the
localization exponent $\nu$. The localization properties of the analytically
tractable $N \gg 1$ theory seem to be continuously connected to those of the
exact quantum Hall plateau transition at $N = 1$.
