Orthogonal run-and-tumble walks

Luca Angelani

Published 2022-09-09Version 1

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 symmetric case, giving general expressions of the probability distribution function (in the Laplace- Fourier domain) and the mean-square displacement. As case studies we treat and discuss (i) isotropic, (ii) alternate, (iii) backward and (iv) forward motions, obtaining, when possible, analytic expression of probability distribution functions in the space-time domain. We discuss at the end also the case of (v) cyclic motion.