A one-dimensional random walk in a multi-zone environment

We study a symmetric random walk (RW) in a one-dimensional environment, formed by several zones of finite width, where the probability of transition between two neighbouring points, and the corresponding diffusion coefficient, are considered to be fixed. We derive analytically the probability of finding a walker at the given position and time. The probability distribution function is found and has no Gaussian form because of the properties of adsorption in the bulk of the zones and the partial reflection at the separation points. The time dependence of the mean squared displacement of a walker is studied too, revealing the transient anomalous behaviour as compared to an ordinary RW.