Random Walks On Finite Convex Sets Of Lattice Points

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Abstract

This paper examines the convergence of nearest-neighbor random walks on convex subsets of the lattices Zd. The main result shows that for fixed d, O(γ2) steps are sufficient for a walk to “get random,” where γ 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.

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