  We investigate the spatial distribution and dynamics of the vortices in
rotating Rayleigh-B\'enard convection in a reduced Rayleigh-number range
$1.3{\le}Ra/Ra_{c}{\le}166$. Under slow rotations ($Ra{\gtrsim}10Ra_{c}$), the
vortices are randomly distributed. The size-distribution of the Voronoi cells
of the vortex centers is well described by the standard $\Gamma$ distribution.
In this flow regime the vortices exhibit Brownian-type horizontal motion. The
probability density functions of the vortex displacements are, however,
non-Gaussian at short time scales. At modest rotating rates
($4Ra_{c}{\le}Ra{\lesssim}10Ra_{c}$) the centrifugal force leads to radial
vortex motions, i.e., warm cyclones (cold anticyclones) moving towards (outward
from) the rotation axis. The mean-square-displacements of the vortices increase
faster than linearly at large time. This super-diffusive behavior can be
satisfactorily explained by a Langevin model incorporating the centrifugal
force. In the rapidly rotating regime ($1.6Ra_{c}{\le}Ra{\le}4Ra_{c}$) the
vortices are densely distributed, with the size-distribution of their Voronoi
cells differing significantly from the standard $\Gamma$ distribution. The
hydrodynamic interaction of neighboring vortices results in formation of vortex
clusters. Inside clusters the correlation of the vortex velocity fluctuations
is scale free, with the correlation length being approximately $30\%$ of the
cluster length. We examine the influence of cluster forming on the dynamics of
individual vortex. Within clusters, cyclones exhibit inverse-centrifugal motion
as they submit to the motion of strong anticyclones, while the velocity for
outward motion of the anticyclones is increased. Our analysis show that the
mobility of isolated vortices, scaled by their vorticity strength, is a simple
power function of the Froude number.
