Generating function matrix for random walks on a simple ladder

Abstract

We consider some basic properties of random walks on a simple ladder including the first and the second moments, the probability of returning to the starting site, the probability of ever reaching a given site, the conditional mean first-passage time to a given site and the expected number of distinct sites visited. These basic properties provide us a great deal of information about mobility, diffusivity and exploration of the random walker. We study these properties by using two different approaches, i.e., the Roerdink and Shuler’s approach and the direct generating function approach. Most of the results are identical to those for one-dimensional lattice except for a renormalization of coefficients.