Cutoff for product replacement on finite groups

Yuval Peres, Ryokichi Tanaka, Alex Zhai

研究成果: Article査読

抄録

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).

本文言語English
ページ(範囲)823-853
ページ数31
ジャーナルProbability Theory and Related Fields
177
3-4
DOI
出版ステータスPublished - 2020 8 1

ASJC Scopus subject areas

  • 分析
  • 統計学および確率
  • 統計学、確率および不確実性

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