Cutoff for product replacement on finite groups

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 ...More