Luke Turvey

Generalised Random Walk in a Random Environment

Random Walk in a Random Environment (RWIRE) is a process where a random transition probability is assigned to each vertex of $\mathbb{Z}^d$. A random walker then evolves according to these transition probabilities. The process for the nearest neighbour 1-dimensional case was studied exhaustively by Solomon '75. In this talk, we give an exposition on partial results from Kalikow '81 concerning the transience and recurrence of the walker in the 2-dimensional RWIRE, featuring non-nearest neighbour transition probabilities.