Orthogonal run-and-tumble walks

Planar run-and-tumble walks with orthogonal directions of motion are considered. After formulating the problem with generic transition probabilities among the orientational states, we focus on the symmetric case, giving general expressions of the probability distribution function (in the Laplace-Fourier domain), the mean-square displacement and the effective diffusion constant in terms of transition rate parameters. As case studies we treat and discuss two classes of motion, alternate/forward and isotropic/backward, obtaining, when possible, analytic expressions of probability distribution functions in the space-time domain. We discuss at the end also the case of cyclic motion. Reduced (enhanced) effective diffusivity, with respect to the standard 2D active motion, is observed in the cyclic and backward (forward) cases.