Monotonicity, Topology, and Convexity of Recurrence in Random Walks

Rupert Li, Elchanan Mossel, Benjamin Weiss

We consider non-homogeneous random walks on the two-dimensional positive quadrant ${\mathbb{N}}^2$ and the one-dimensional slab $\{0,1,\dots ,k\}\times \mathbb{N}$. In the 1960's the f…