@article{a85498ef759047e1a9bcdd56c10b971c,
title = "Cutoff for product replacement on finite groups",
abstract = "We analyze a Markov chain, known as the product replacement chain, on the set of generating n-tuples of a fixed finite group G. We show that as n→ ∞, the total-variation mixing time of the chain has a cutoff at time 32nlogn with window of order n. This generalizes a result of Ben-Hamou and Peres (who established the result for G= Z/ 2) and confirms a conjecture of Diaconis and Saloff-Coste that for an arbitrary but fixed finite group, the mixing time of the product replacement chain is O(nlog n).",
keywords = "Cutoff phenomenon, Markov chain, Mixing time, Product replacement algorithm",
author = "Yuval Peres and Ryokichi Tanaka and Alex Zhai",
note = "Funding Information: This work was initiated while R.T. and A.Z. were visiting Microsoft Research in Redmond. They thank Microsoft Research for the hospitality. R.T. was also visiting the University of Washington in Seattle and thanks Professor Christopher Hoffman for making his visit possible. R.T. is supported by JSPS Grant-in-Aid for Young Scientists (B) 17K14178 and partially by JST, ACT-X Grant Number JPMJAX190J, Japan. A.Z. is supported by a Stanford Graduate Fellowship. The authors thank an anonymous referee for helpful comments. Funding Information: This work was initiated while R.T. and A.Z. were visiting Microsoft Research in Redmond. They thank Microsoft Research for the hospitality. R.T. was also visiting the University of Washington in Seattle and thanks Professor Christopher Hoffman for making his visit possible. R.T. is supported by JSPS Grant-in-Aid for Young Scientists (B) 17K14178 and partially by JST, ACT-X Grant Number JPMJAX190J, Japan. A.Z. is supported by a Stanford Graduate Fellowship. The authors thank an anonymous referee for helpful comments. ",
year = "2020",
month = aug,
day = "1",
doi = "10.1007/s00440-020-00962-1",
language = "English",
volume = "177",
pages = "823--853",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "3-4",
}