  Disc-driven planet migration is integral to the formation of planetary
systems. In standard, gas-dominated protoplanetary discs, low-mass planets or
planetary cores undergo rapid inwards migration and are lost to the central
star. However, several recent studies indicate that the solid component in
protoplanetary discs can have a significant dynamical effect on disc-planet
interaction, especially when the solid-to-gas mass ratio approaches unity or
larger and the dust-on-gas drag forces become significant. As there are several
ways to raise the solid abundance in protoplanetary discs, for example through
disc winds and dust-trapping in pressure bumps, it is important to understand
how planets migrate through a dusty environment. To this end, we study planet
migration in dust-rich discs via a systematic set of high-resolution,
two-dimensional numerical simulations. We show that the inwards migration of
low-mass planets can be slowed down by dusty dynamical corotation torques. We
also identify a new regime of stochastic migration applicable to discs with
dust-to-gas mass ratios $\gtrsim 0.3$ and particle Stokes numbers $\gtrsim
0.03$. In these cases, disc-planet interaction leads to the continuous
development of small-scale, intense dust vortices that scatter the planet,
which can potentially halt or even reverse the inwards planet migration. We
briefly discuss the observational implications of our results and highlight
directions for future work.
