  Numerical simulations show that the migration of growing planetary cores may
be dominated by turbulent fluctuations in the protoplanetary disk, rather than
by any mean property of the flow. We quantify the impact of this stochastic
core migration on the formation time scale and core mass of giant planets at
the onset of runaway gas accretion. For standard Solar Nebula conditions, the
formation of Jupiter can be accelerated by almost an order of magnitude if the
growing core executes a random walk with an amplitude of a few tenths of an au.
A modestly reduced surface density of planetesimals allows Jupiter to form
within 10 Myr, with an initial core mass below 10 Earth masses, in better
agreement with observational constraints. For extrasolar planetary systems, the
results suggest that core accretion could form massive planets in disks with
lower metallicities, and shorter lifetimes, than the Solar Nebula.
