  In this paper, a lower bound on the capacity of wireless ad hoc erasure
networks is derived in closed form in the canonical case where $n$ nodes are
uniformly and independently distributed in the unit area square. The bound
holds almost surely and is asymptotically tight. We assume all nodes have fixed
transmit power and hence two nodes should be within a specified distance $r_n$
of each other to overcome noise. In this context, interference determines
outages, so we model each transmitter-receiver pair as an erasure channel with
a broadcast constraint, i.e. each node can transmit only one signal across all
its outgoing links. A lower bound of $\Theta(n r_n)$ for the capacity of this
class of networks is derived. If the broadcast constraint is relaxed and each
node can send distinct signals on distinct outgoing links, we show that the
gain is a function of $r_n$ and the link erasure probabilities, and is at most
a constant if the link erasure probabilities grow sufficiently large with $n$.
Finally, the case where the erasure probabilities are themselves random
variables, for example due to randomness in geometry or channels, is analyzed.
We prove somewhat surprisingly that in this setting, variability in erasure
probabilities increases network capacity.
