  We investigate the kinematic evolution of planetesimals in self-gravitating
discs, combining Smoothed Particle Hydrodynamical (SPH) simulations of the disc
gas with a gravitationally coupled population of test particle planetesimals.
We find that at radii of 10s of au (which is where we expect planetesimals to
be possibly formed in such discs) the planetesimals' eccentricities are rapidly
pumped to values $>$ 0.1 within the timescales for which the disc is in the
self-gravitating regime. The high resulting velocity dispersion and the lack of
planetesimal concentration in the spiral arms means that the collision
timescale is very long and that the effect of those collisions that do occur is
destructive rather than leading to further planetesimal growth. We also use the
SPH simulations to calibrate Monte Carlo dynamical experiments: these can be
used to evolve the system over long timescales and can be compared with
analytical solutions of the diffusion equation in particle angular momentum
space. We find that if planetesimals are only formed in a belt at large radius
then there is significant scattering of objects to small radii; nevertheless
the majority of planetesimals remain at large radii. If planetesimals indeed
form at early evolutionary stages, when the disc is strongly self-gravitating,
then the results of this study constrain their spatial and kinematic
distribution at the end of the self-gravitating phase.
