Random Walks On Finite Convex Sets Of Lattice Points

Balint Virag

Journal of Theoretical Probability, 1998, vol. 11, issue 4, 935-951

Abstract: Abstract This paper examines the convergence of nearest-neighbor random walks on convex subsets of the latticesℤd. The main result shows that for fixedd, 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.

Keywords: Convexity; random walks; convergence rate; lattices (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022612814891

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