  We apply the theory of random Schr\"odinger operators to the analysis of
multi-users communication channels similar to the Wyner model, that are
characterized by short-range intra-cell broadcasting. With $H$ the channel
transfer matrix, $HH^\dagger$ is a narrow-band matrix and in many aspects is
similar to a random Schr\"odinger operator. We relate the per-cell sum-rate
capacity of the channel to the integrated density of states of a random
Schr\"odinger operator; the latter is related to the top Lyapunov exponent of a
random sequence of matrices via a version of the Thouless formula. Unlike
related results in classical random matrix theory, limiting results do depend
on the underlying fading distributions. We also derive several bounds on the
limiting per-cell sum-rate capacity, some based on the theory of random
Schr\"odinger operators, and some derived from information theoretical
considerations. Finally, we get explicit results in the high-SNR regime for
some particular cases.
