Bulk-mediated diffusion on a planar surface: full solution
  We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random walk approach we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover we study the long-time dynamics for the surface motion. 
Aleksei V. Chechkin, Irwin M. Zaid, Michael A. Lomholt, Igor M.   Sokolov, Ralf Metzler
cond-mat.stat-mech