Cutoff for the Adjacent Transposition Shuffle on a Cycle

Colin Defant

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arXiv · 2609.40076

Cutoff for the Adjacent Transposition Shuffle on a Cycle

Colin Defant

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Abstract

In the adjacent transposition shuffle on a cycle, $n$ distinct cards are placed at the vertices of a cycle, and adjacent cards swap positions according to independent Poisson clocks of rate 1. We prove that this Markov chain exhibits total variation cutoff at time $n^2\log n/(8π^2)$, with a window of order at most $n^2\log\log n$.

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Colin Defant. 2026-09-30. Cutoff for the Adjacent Transposition Shuffle on a Cycle. https://arxiv.org/abs/2609.40076

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