# Cutoff for product replacement on finite groups

arXiv: Probability, 2018.

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 $n rightarrow infty$, the total-variation mixing time of the chain has a cutoff at time $frac{3}{2} n log n$ with window of order $n$. This generalizes a result of Ben-Hamou and Peres (who est...More

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