  This paper derives a lower bound to the per-node throughput achievable by a
wireless network when n source-destination pairs are randomly distributed
throughout a disk of radius $n^\gamma$, $ \gamma \geq 0$, propagation is
modeled by attenuation of the form $1/(1+d)^\alpha$, $\alpha >2$, and
successful transmission occurs at a fixed rate W when received signal to noise
and interference ratio is greater than some threshold $\beta$, and at rate 0
otherwise. The lower bound has the form $n^{1-\gamma}$ when $\gamma < 1/2$, and
$(n \ln n)^{-1/2}$ when $\gamma \geq 1/2$. The methods are similar to, but
somewhat simpler than, those in the seminal paper by Gupta and Kumar.
