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Entropy, isoperimetry and the total variation profile of random walks
The total variation profile $\mathrm{TV}_n$ of a random walk measures how far its distribution at time $n$ is from being invariant under the generators. Three lower bounds are given: an elementary bound $\mathrm{TV}_n \geq 1/\big(44\,L(n)\big)$ in terms of the speed $L(n)$; a bound by the entropy in
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