  Let $\Gamma$ be a finitely generated group equipped with a symmetric and
nondegenerate probability measure $\mu$ with finite second moment, and $Y$ a
CAT(0) space which is either proper or of finite telescopic dimension. We show
that if an isometric action of $\Gamma$ on $Y$ has vanishing rate of escape
with respect to $\mu$ and does not fix a point in the boundary at infinity of
$Y$, then there exists a flat subspace in $Y$ which is left invariant under the
action of $\Gamma$. In the proof of this result, an equivariant $\mu$-harmonic
map from $\Gamma$ into $Y$ plays an important role.
