  Let $G$ be a finite connected graph, and let $T$ be a spanning tree of $G$
chosen uniformly at random. The work of Kirchhoff on electrical networks can be
used to show that the events $e_1 \in T$ and $e_2 \in T$ are negatively
correlated for any distinct edges $e_1$ and $e_2$. What can be said for such
events when the underlying matroid is not necessarily graphic? We use Hodge
theory for matroids to bound the correlation between the events $e \in B$,
where $B$ is a randomly chosen basis of a matroid. As an application, we prove
Mason's conjecture that the number of $k$-element independent sets of a matroid
forms an ultra-log-concave sequence in $k$.
