7 papers
Random Walks in Random Environments with Rare Anomalies
Daniel J. Slonim
We study random walks in i.i.d. random environments on when there are two basic types of vertices, which we call "blue" and "red". Each color represents a different…
On total weight exiting finite, strongly connected sets in shift-invariant weighted directed graphs on
Daniel J. Slonim
For a shift-invariant weighted directed graph with vertex set , we examine the minimal weight exiting a finite, strongly connected set of vertices. Although …
Ballisticity of Random walks in Random Environments on with Bounded Jumps
Daniel J. Slonim
We characterize ballistic behavior for general i.i.d. random walks in random environments on with bounded jumps. The two characterizations we provide do not use unifor…
A zero-one law for random walks in random environments on with bounded jumps
Daniel J. Slonim
This paper has two main results, which are connected through the fact that the first is a key ingredient in the second. Both are extensions of results concerning directional transi…
Random Walks in Dirichlet Random Environments on with Bounded Jumps
Daniel J. Slonim
We examine a class of random walks in random environments on with bounded jumps, a generalization of the classic one-dimensional model. The environments we study have…
Interleaving of path sets
William C. Abram, Jeffrey C. Lagarias, Daniel Slonim
Path sets are spaces of one-sided infinite symbol sequences corresponding to the one-sided infinite walks beginning at a fixed initial vertex in a directed labeled graph. Path sets…
Decimation and Interleaving Operations in One-Sided Symbolic Dynamics
William C. Abram, Jeffrey C. Lagarias, Daniel J. Slonim
This paper studies subsets of one-sided shift spaces on a finite alphabet. Such subsets arise in symbolic dynamics, in fractal constructions, and in number theory. We study a famil…