  Consider $n$ points distributed uniformly in $[0,1]^d$. Form a graph by
connecting two points if their mutual distance is no greater than $r(n)$. This
gives a random geometric graph, $\gnrn$, which is connected for appropriate
$r(n)$. We show that the spectral measure of the transition matrix of the
simple random walk (\abbr{srw}) on $\gnrn$ is concentrated, and in fact
converges to that of the graph on the deterministic grid.
