Mixing Times for Random Walks on Finite Lamplighter Groups
نویسندگان
چکیده
منابع مشابه
Mixing times for Random Walks on Finite Lamplighter Groups
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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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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A geometric random graph, G(n, r), is formed as follows: place n nodes uniformly at random onto the surface of the d-dimensional unit torus and connect nodes which are within a distance r of each other. The G(n, r) has been of great interest due to its success as a model for ad-hoc wireless networks. It is well known that the connectivity of G(n, r) exhibits a threshold property: there exists a...
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Markov chains on finite sets are used in a great variety of situations to approximate, understand and sample from their limit distribution. A familiar example is provided by card shuffling methods. From this viewpoint, one is interested in the “mixing time” of the chain, that is, the time at which the chain gives a good approximation of the limit distribution. A remarkable phenomenon known as t...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2004
ISSN: 1083-6489
DOI: 10.1214/ejp.v9-198