Random Walks On Finite Convex Sets Of Lattice Points

This paper examines the convergence of nearest-neighbor random walks on convex subsets of the lattices^d. The main result shows that for fixedd, O(²) steps are sufficient for a walk to get random, where is the diameter of the set. Toward this end a new definition of convexity is introduced for subsets of lattices, which has many important properties of the concept of convexity in Euclidean spaces.