  Substantial orbital migration of massive planets may occur in most extrasolar
planetary systems. Since migration is likely to occur after a significant
fraction of the dust has been locked up into planetesimals, ubiquitous
migration could reduce the probability of forming terrestrial planets at radii
of the order of 1 au. Using a simple time dependent model for the evolution of
gas and solids in the disk, I show that replenishment of solid material in the
inner disk, following the inward passage of a giant planet, is generally
inefficient. Unless the timescale for diffusion of dust is much shorter than
the viscous timescale, or planetesimal formation is surprisingly slow, the
surface density of planetesimals at 1 au will typically be depleted by one to
two orders of magnitude following giant planet migration. Conceivably,
terrestrial planets may exist only in a modest fraction of systems where a
single generation of massive planets formed and did not migrate significantly.
