منابع مشابه
Spectral Computations on Lamplighter Groups and Diestel-leader Graphs
The Diestel-Leader graph DL(q, r) is the horocyclic product of the homogeneous trees with respective degrees q+1 and r+1. When q = r, it is the Cayley graph of the lamplighter group (wreath product) Zq≀Z with respect to a natural generating set. For the “Simple random walk” (SRW) operator on the latter group, Grigorchuk and Żuk and Dicks and Schick have determined the spectrum and the (on-diago...
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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 limi...
متن کاملLamplighters, 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...
متن کاملSome Metric Properties of Automorphisms of Groups
Study of the dynamics of automorphisms of a group is usually focused on their growth and/or finite orbits, including fixed points. In this paper, we introduce properties of a different kind; using somewhat informal language, we call them metric properties. Two principal characteristics of this kind are called here the “curl” and the “flux”; there seems to be very little correlation between thes...
متن کاملMetric properties of Baumslag-Solitar groups
We compute estimates for the word metric of Baumslag–Solitar groups in terms of the Britton’s lemma normal form. As a corollary, we find lower bounds for the growth rate for the groups BS(p, q), with 1 < p ≤ q.
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2013
ISSN: 0026-2285
DOI: 10.1307/mmj/1370870377