Dynamics of lattice random walk within regions composed of different media and interfaces

Abstract We study the lattice random walk dynamics in a heterogeneous space of two media separated by an interface and having different diffusivity bias. Depending on position interface, there exist exclusive ways to model dynamics: (a) Type A whereby is placed between points, (b) B point. For both types, we obtain exact results for one-dimensional generating function Green’s or propagator composite system unbounded domain as well domains confined with reflecting, absorbing, mixed boundaries. case reflecting confinement absence bias, steady-state probability shows step-like behavior dynamics, while it uniform dynamics. also derive explicit expressions first-passage mean time, compare hitting time dependence single target. Finally, considering continuous-space continuous-time limit propagator, boundary conditions at interface. At flux same, density discontinuous continuous . latter generalized version so-called leather condition appropriate limit.