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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.