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 the n-step transition probabilities of the simple random walk is determined.
Bertacchi, D. (2001). Random walks on Diestel-Leader graphs. ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 71, 205-224 [10.1007/BF02941472].
Random walks on Diestel-Leader graphs
Bertacchi, D
2001
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 the n-step transition probabilities of the simple random walk is determined.
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