2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117914We 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.12 PagesProbabilityCombinatorics60J10 (Primary) ; 60J27; 68W20 (Secondary)text