Total variation and separation cutoffs are not equivalent and neither one implies the other

@inproceedings{Hermon2016TotalVA,
  title={Total variation and separation cutoffs are not equivalent and neither one implies the other},
  author={Jonathan Hermon and Hubert Lacoin and Yuval Peres},
  year={2016}
}
  • Jonathan Hermon, Hubert Lacoin, Yuval Peres
  • Published 2016
  • Mathematics
  • The cutoff phenomenon describes the case when an abrupt transition occurs in the convergence of a Markov chain to its equilibrium measure. There are various metrics which can be used to measure the distance to equilibrium, each of which corresponding to a different notion of cutoff. The most commonly used are the total-variation and the separation distances. In this note we prove that the cutoff for these two distances are not equivalent by constructing several counterexamples which display… CONTINUE READING

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