On the asymptotic behavior of random walks on an anisotropic lattice

A random walk on a two-dimensional lattice with homogeneous rows and inhomogeneous columns, which could serve as a model for the study of some transport phemonema, is discussed. Subject to an asymptotic density condition on the columns it is shown that the horizontal motion of the walk is asymptotically like that of rescaled Brownian motion. Various consequences of this are derived including central limit, iterated logarithm, and mean square displacement results for the horizontal component of the walk.