  Torque fluctuations due to magnetorotational turbulence in proto-planetary
disks may greatly influence the migration patterns and survival probabilities
of nascent planets. Provided that the turbulence is a stationary stochastic
process with finite amplitude and correlation time, the resulting diffusive
migration can be described with a Fokker-Planck equation, which we reduce to an
advection-diffusion equation. We calibrate the coefficients with existing
turbulent-disk simulations and mean-migration estimates, and solve the equation
both analytically and numerically. Diffusion tends to dominate over advection
for planets of low-mass and those in the outer regions of proto-planetary
disks, whether they are described by the Minimum Mass Solar Nebula (MMSN) or by
T-Tauri alpha disks. Diffusion systematically reduces the lifetime of most
planets, yet it allows a declining fraction of them to survive for extended
periods of time at large radii. Mean planet lifetimes can even be formally
infinite (e.g. in an infinite steady MMSN), though median lifetimes are always
finite. Surviving planets may linger near specific radii where the combined
effects of advection and diffusion are minimized, or at large radii, depending
on model specifics. The stochastic nature of migration in turbulent disks
challenges deterministic planet formation scenarios and suggests instead that a
wide variety of planetary outcomes are possible from similar initial
conditions. This would contribute to the diversity of (extrasolar) planetary
systems.
