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Spectral Computations on Lamplighter Groups and Diestel-Leader Graphs

Journal of Fourier Analysis and Applications, no. 2 (2005): 175-202

Cited: 63|Views20

Abstract

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 Zuk, and...More

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