Abstract
We investigate various features of a quite new family of graphs, introduced as a possible example of vertex-transitive graph not roughly isometric with a Cayley graph of some finitely generated group. We exhibit a natural compactification and study a large class of random walks, proving theorems concerning almost sure convergence to the boundary, a strong law of large numbers and a central limit theorem. The asymptotic type of then-step transition probabilities of the simple random walk is determined.
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Bertacchi, D. Random walks on diestel-leader graphs. Abh.Math.Semin.Univ.Hambg. 71, 205–224 (2001). https://doi.org/10.1007/BF02941472
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DOI: https://doi.org/10.1007/BF02941472