Journal of Statistical Physics, Vol. 21, No. 5, 1979 Random Walks on Periodic and Random Lattices. II. Random Walk Properties via Generating Function Techniques V. Seshadri, 1 Katja Lindenberg, 1 and Kurt E. Shuler 1 Received April 17, 1979 We investigate the random walk properties of a class of two-dimensional lattices with two different types of columns and discuss the dependence of the properties on the densities and detailed arrangements of the columns. We show that the row and column components of the mean square dis- placement are asymptotically independent of the details of the arrangement of columns. We reach the same conclusion for some other random walk properties (return to the origin and number of distinct sites visited) for various periodic arrangements of a given relative density of the two types of columns. We also derive exact asymptotic results for the occupation probabilities of the two types of distinct sites on our lattices which validate the basic conjecture on bond and step ratios made in the preceding paper in this series. KEY WORDS: Random walks; periodic lattices; random lattices; generating function techniques. 1. INTRODUCTION This is the third in a series of papers on random walks in a class of lattices that might serve as models for the study of transport properties in a variety of anisotropic and disordered systems. We consider two-dimensional lattices in which the transition probabilities may be different for sites lying in different columns. A special case of our model, already analyzed in detail in Refs. 1 and 2 (hereafter referred to as A and B) is one in which the walker can always step to nearest neighbor sites in any row but can step to nearest neighbor sites in a column only for certain specified columns. In this paper we Supported in part by a grant from Charles and Ren6e Taubman and by the National Science Foundation, Grant CHE 78-21460. 1 Department of Chemistry, University of California--San Diego, La Jolla, California. fi17 0022-4715/79] 1100-0517503.00]0 91979 Plenum Publishing Corporation