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A Note On Recurrence, Amenability, and the Universal Cover Of Graphs
Abstract

SAM NORTHSHIELD

Given a regular graph G, and its unversal covering tree T, we give conditions which relate recurrence and amenability of G to the size of a certain subset R of the Martin boundary of T
In particular, G is recurrent if and only if R has full harmonic measure; G is amenable if and only if R has full Hausdorff demension.




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