  (Abridged) Planetesimals embedded in a protoplanetary disc are stirred by
gravitational torques exerted by density fluctuations in the surrounding
turbulence. In particular, planetesimals in a disc supporting fully developed
magneto-rotational turbulence are readily excited to velocity dispersions above
the threshold for catastrophic disruption, halting planet formation. We aim to
examine the stirring of planetesimals lying instead in a magnetically-decoupled
midplane dead zone, stirred only by spiral density waves propagating out of the
disc's magnetically-coupled turbulent surface layers. We extend previous
studies to include a wider range of disc models, and explore the effects of
varying the disc column density and external magnetic field strength. [...] The
strength of the stirring is found to be independent of the gas surface density,
which is contrary to the increase with disc mass expected from a simple linear
wave picture. The discrepancy arises from the shearing out of density waves as
they propagate into the dead zone, resulting in density structures near the
midplane that exert weaker stochastic torques on average. We provide a simple
analytic fit to our numerically obtained torque amplitudes that accounts for
this effect. The stirring on the other hand depends sensitively on the net
vertical magnetic flux, up to a saturation level above which magnetic forces
dominate in the turbulent layers. For the majority of our models, the
equilibrium planetesimal velocity dispersions lie between the thresholds for
disrupting strong and weak aggregates, suggesting that collision outcomes will
depend on material properties. However, discs with relatively weak magnetic
fields yield reduced stirring, and their dead zones provide safe-havens even
for the weakest planetesimals against collisional destruction.
