Random Walks on Diestel-leader Graphs
نویسنده
چکیده
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.
منابع مشابه
Lamplighters, Diestel-Leader Graphs, Random Walks, and Harmonic Functions
The lamplighter group over Z is the wreath product Zq ≀ Z. With respect to a natural generating set, its Cayley graph is the Diestel-Leader graph DL(q, q). We study harmonic functions for the “simple” Laplacian on this graph, and more generally, for a class of random walks on DL(q, r), where q, r ≥ 2. The DL-graphs are horocyclic products of two trees, and we give a full description of all posi...
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