  Lyons and Sullivan have shown how to discretize harmonic functions on a
Riemannian manifold $M$ whose Brownian motion satisfies a certain recurrence
property called $\ast$-recurrence. We study analogues of this discretization
for tensor fields which are harmonic in the sense of the covariant Laplacian.
We show that, under certain restrictions on the holonomy of the connection, the
lifted diffusion on the orthonormal frame bundle has the same $\ast$-recurrence
property as the original Brownian motion. This observation permits us to reduce
to the discretization of ordinary harmonic functions by a device called
scalarization.
