A Tight Bound for the Lamplighter Problem

Details A Tight Bound for the Lamplighter Problem A Tight Bound for the Lamplighter Problem

2006-10-10

arxiv.org/abs/math/0610345v1

Mathematics

Probability

12 Pages

Scientific paper

We settle an open problem, raised by Y. Peres and D. Revelle, concerning the
$L^2$ mixing time of the random walk on the lamplighter graph. We also provide
general bounds relating the entropy decay of a Markov chain to the separation
distance of the chain, and show that the lamplighter graphs once again provide
examples of tightness of our results.

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