Harmonic Analysis of Finite Lamplighter Random Walks
نویسندگان
چکیده
منابع مشابه
Harmonic analysis of finite lamplighter random walks
Recently, several papers have been devoted to the analysis of lamplighter random walks, in particular when the underlying graph is the infinite path Z. In the present paper, we develop a spectral analysis for lamplighter random walks on finite graphs. In the general case, we use the C2-symmetry to reduce the spectral computations to a series of eigenvalue problems on the underlying graph. In th...
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Suppose we are given an infinite, finitely generated group G and a transient random walk with bounded range on the wreath product (Z/2Z) ≀ G, such that its projection on G is transient. This random walk can be interpreted as a lamplighter random walk, where there is a lamp at each element of G, which can be switched on and off, and a lamplighter walks along G and switches lamps randomly on and ...
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Given a finite graph G, a vertex of the lamplighter graph G♦ = Z2 o G consists of a zero-one labeling of the vertices of G, and a marked vertex of G. For transitive G we show that, up to constants, the relaxation time for simple random walk in G♦ is the maximal hitting time for simple random walk in G, while the mixing time in total variation on G♦ is the expected cover time on G. The mixing ti...
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We determine all positive harmonic functions for a large class of “semiisotropic” random walks on the lamplighter group, i.e., the wreath product Zq ≀Z, where q ≥ 2. This is possible via the geometric realization of a Cayley graph of that group as the Diestel-Leader graph DL(q, q). More generally, DL(q, r) (q, r ≥ 2) is the horocyclic product of two homogeneous trees with respective degrees q+1...
متن کاملThe Poisson Boundary of Lamplighter Random Walks on Trees
Let Tq be the homogeneous tree with degree q + 1 ≥ 3 and G a finitely generated group whose Cayley graph is Tq. The associated lamplighter group is the wreath product Zr ≀ G, where Zr is the cyclic group of order r. For a large class of random walks on this group, we prove almost sure convergence to a natural geometric boundary. If the probability law governing the random walk has finite first ...
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ژورنال
عنوان ژورنال: Journal of Dynamical and Control Systems
سال: 2008
ISSN: 1079-2724,1573-8698
DOI: 10.1007/s10883-008-9038-8