ABSTRACT
This chapter discusses two important classes of random walk type processes which are frequently used in applied probability. The first class of models relates to random walks on lattices and graphs. The second one is related to urn processes, such as the Ehrenfest and the Polya urn models. The chapter focuses on the long time behavior of the Single Rear Wheel in terms of the dimension and the analysis of Markov chains on countable state spaces. It discusses the simple exclusion process can be represented by a random walk on the set, where stands for some set of vertices of some finite graph of the same form as the one.
