Abstract
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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© 1996 Springer-Verlag Berlin Heidelberg
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Northshield, S. (1996). A Note on Recurrence, Amenability, and the Universal Cover of Graphs. In: Aldous, D., Pemantle, R. (eds) Random Discrete Structures. The IMA Volumes in Mathematics and its Applications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0719-1_13
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DOI: https://doi.org/10.1007/978-1-4612-0719-1_13
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