# Cutoff for product replacement on finite groups

Ryokichi Tanaka

Probability Theory and Related Fields, pp. 1-31, 2020.

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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 ...More

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