  The large scale infall of galaxies around massive clusters provides a
potentially powerful diagnostic of structure growth, dark energy, and
cosmological deviations from General Relativity. We develop and test a method
to recover galaxy infall kinematics (GIK) from measurements of the
redshift-space cluster-galaxy cross-correlation function \xi_{cg}(r_p,r_\pi).
Using galaxy and halo samples from the Millennium simulation, we calibrate an
analytic model of the galaxy kinematic profiles comprised of a virialized
component with an isotropic Gaussian velocity distribution and an infall
component described by a skewed 2D t-distribution with a characteristic infall
velocity v_r and separate radial and tangential dispersions. We show that
convolving the real-space cross-correlation function with this velocity
distribution accurately predicts the redshift-space \xi_{cg}, and we show that
measurements of \xi_{cg} can be inverted to recover the four distinct elements
of the GIK profiles. These in turn provide diagnostics of cluster mass
profiles, and we expect the characteristic infall velocity v_r(r) in particular
to be insensitive to galaxy formation physics that can affect velocity
dispersions within halos. As a proof of concept we measure \xi_{cg} for rich
galaxy groups in the Sloan Digital Sky Survey and recover GIK profiles for
groups in two bins of central galaxy stellar mass. The higher mass bin has a
v_r(r) curve very similar to that of 10^{14} Msun halos in the Millennium
simulation, and the recovered kinematics follow the expected trends with mass.
GIK modeling of cluster-galaxy cross-correlations can be a valuable complement
to stacked weak lensing analyses, allowing novel tests of modified gravity
theories that seek to explain cosmic acceleration.
