  Galaxy cluster surveys compiled via the Sunyaev-Zeldovich Effect have the
potential to place strong constraints on cosmology, and in particular the
nature of dark energy. Here we consider cluster velocity surveys using kinetic
Sunyaev-Zeldovich measurements. Cluster velocities closely trace the
large-scale velocity field independent of cluster mass; we demonstrate that two
useful cluster velocity statistics are nearly independent of cluster mass, in
marked contrast to cluster number count statistics. On the other hand, cluster
velocity determinations from three-band observations of Sunyaev-Zeldovich
distortions can require additional cluster data or assumptions, and are
complicated by microwave emission from dusty galaxies and radio sources, which
may be correlated with clusters. Systematic errors in velocity due to these
factors can give substantial biases in determination of dark energy parameters,
although large cluster velocity surveys will contain enough information that
the errors can be modeled using the data itself, with little degradation in
cosmological constraints.
