  The (maximum receiver-centric) interference of a geometric graph (von
Rickenbach etal (2005)) is studied. It is shown that, with high probability,
the following results hold for a set, V, of n points independently and
uniformly distributed in the unit d-cube, for constant dimension d: (1) there
exists a connected graph with vertex set V that has interference O((log
n)^{1/3}); (2) no connected graph with vertex set V has interference o((log
n)^{1/4}); and (3) the minimum spanning tree of $V$ has interference
Theta((\log n)^{1/2}).
