Discrete Scattering and Simple and Nonsimple Face-Homogeneous Random Walks

Abstract

In this article we will derive some results for characterizing the almost closed sets of a face-homogeneous random walk. We will present a conjecture on the relation between discrete scattering of the fluid limit and the absence of nonatomic almost closed sets. We will illustrate the conjecture with random walks with both simple and nonsimple decomposition into almost closed sets.