  We analyze fading interference relay networks where M single-antenna
source-destination terminal pairs communicate concurrently and in the same
frequency band through a set of K single-antenna relays using half-duplex
two-hop relaying. Assuming that the relays have channel state information
(CSI), it is shown that in the large-M limit, provided K grows fast enough as a
function of M, the network "decouples" in the sense that the individual
source-destination terminal pair capacities are strictly positive. The
corresponding required rate of growth of K as a function of M is found to be
sufficient to also make the individual source-destination fading links converge
to nonfading links. We say that the network "crystallizes" as it breaks up into
a set of effectively isolated "wires in the air". A large-deviations analysis
is performed to characterize the "crystallization" rate, i.e., the rate (as a
function of M,K) at which the decoupled links converge to nonfading links. In
the course of this analysis, we develop a new technique for characterizing the
large-deviations behavior of certain sums of dependent random variables. For
the case of no CSI at the relay level, assuming amplify-and-forward relaying,
we compute the per source-destination terminal pair capacity for M,K converging
to infinity, with K/M staying fixed, using tools from large random matrix
theory.
